Inclusion Criteria:  Subject must meet all of the following applicable inclusion criteria to participate in this study:  Written informed consent and HIPAA authorization for release of personal health information must be obtained either from the subject or their representative. See 3.1.12. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. Age ≥ 18 years at the time of consent. ECOG Performance Status of 0-1. Histologically proven locally advanced, metastatic, or unresectable hepatocellular carcinoma that has not received prior systemic therapy. Note: if no prior histologic diagnosis exists, fresh biopsy will be requested if it is both safe and feasible. If fresh biopsy is not safe and feasible, imaging criteria may be used for diagnosis as per AASLD criteria in cirrhotic patients (please see www.aasld.org for up to date guidelines). Child Pugh Class B7 liver dysfunction or cirrhosis (please see Appendix 3). Note: patients with clinically meaningful ascites or encephalopathy are ineligible (please see protocol). At least 1 untreated measurable lesion according to RECIST 1.1. Willingness to undergo fresh tumor biopsy at baseline if safe and feasible. Note: archival tissue may be used at baseline provided histologic diagnosis was made and sufficient tissue is available for NGS analysis. NGS analysis must be requested from archival tissue or fresh biopsy (if applicable) as per standard of care. Foundation One CDX is the preferred platform. Prior NGS sequencing results (including from another platform) will be accepted if both histologic diagnosis and NGS sequencing were previously obtained (please see protocol). Demonstrate adequate bone marrow and organ function as defined in the table in the protocol For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of < 1% per year during the treatment period and for at least 5 months after the last dose of atezolizumab, or 6 months after the last dose of bevacizumab. See also the protocol for definition of childbearing potential. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use effective contraceptive measures. Men with female partners of childbearing potential must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of < 1% per year during the treatment period and for 6 months after the last dose of bevacizumab. With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for 6 months after the last dose of bevacizumab to avoid exposing the embryo. See also the protocol for additional information. As determined by the enrolling physician or protocol designee, ability of the subject to understand a written informed consent document, and ability and willingness to comply with study procedures for the entire length of the study. Patients with impaired decision-making capacity (IDMC) who have a close caregiver or legally authorized representative (LAR) and/or family member available are also eligible.  Exclusion Criteria:  Subjects meeting any of the criteria below may not participate in the study:  Histologic diagnosis of fibrolamellar or sarcomatoid HCC or mixed cholangiocarcinoma-HCC. Patients who have had chemotherapy, definitive radiation, biological cancer therapy, or investigational agent/device within 21 days of first planned dose of study therapy (within 14 days for palliative radiation). Patients who have had major surgery within 4 weeks of start of study therapy or anticipation of need for a major surgical procedure during the study. Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities > CTCAE Grade 1) with the exception of alopecia or neuropathy. Patients who have received prior systemic therapy for HCC. Patients who have received prior immunotherapy. Patients with clinically meaningful ascites, defined as ascites requiring non-pharmacologic intervention (e.g. paracentesis) to maintain symptomatic control within 3 months prior to the first dose of study treatment. Note: Patients with ascites who require pharmacologic intervention (e.g. diuretics) to maintain symptomatic control and who have been on stable doses of diuretics for 2 months days prior to the first dose of study treatment are eligible. Patients with clinically meaningful encephalopathy, defined as a history of hepatic encephalopathy within 12 months prior to first dose of study treatment or requirement for medications to prevent or control encephalopathy (e.g. lactulose, rifaximin).  Any of the following additional high-risk features:  Patients with untreated or incompletely treated esophageal and/or gastric varices with bleeding or high risk for bleeding. Note: Patients must undergo an esophagogastroduodenoscopy (EGD), and all size of varices (small to large) must be assessed and treated per local standard of care prior to enrollment. Patients who have undergone an EGD with appropriate management of varices (if applicable) within 6 months of prior to initiation of study treatment do not need to repeat the procedure. History of esophageal and/or gastric hemorrhage within 3 months prior to study treatment. History of hemoptysis (< 2.5 mL of bright red blood per episode) within 1 month prior to study treatment. History of intracranial hemorrhage within 1 month prior to study treatment. History of abdominal or tracheoesophageal fistula, gastrointestinal (GI) perforation, or intra-abdominal abscess within 6 months prior to initiation of study treatment. Evidence of abdominal free air that is not explained by paracentesis or recent surgical procedure. Serious, non-healing or dehiscing wound, active ulcer, or untreated bone fracture within 30 days prior to start of study treatment. Metastatic disease that involves major airways or blood vessels. Patients with vascular invasion of the portal or hepatic veins may be enrolled. Significant vascular disease (e.g. aortic aneurysm requiring surgical repair) or vasculitis within 6 months prior to initiation of study treatment. History of arterial thrombotic event (e.g. myocardial infarction, unstable angina, cerebrovascular accident, or transient ischemic attack) within 6 months prior to initiation of study treatment. Chronic or recent (within 10 days of first dose of study treatment) use of aspirin > 325 mg/day, dipyramidaole, ticlopidine, clopidogrel, or dilostazol. Note: Use of aspirin 81 mg/day is allowed. History of venous thromboembolic event (e.g. deep vein thrombosis, pulmonary embolism, portal vein thrombosis, or any other significant thromboembolism) within 3 months prior to initiation of study treatment. Note: venous port or catheter thrombosis or superficial venous thrombosis are not considered significant. Chronic or recent (within 10 days of first dose of study treatment) use of full-dose oral or parenteral anticoagulants or thrombolytic agents for therapeutic purposes. Note: prophylactic anticoagulation for patency of venous access devices is allowed provided the activity of the agent results in an INR < 1.5x ULN and aPTT is within normal limits within 14 days of start of study treatment. Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation) Core biopsy or other minor surgical procedure within 3 days prior to the first dose of bevacizumab. History of intestinal obstruction. Note: Patients with previous intestinal obstruction may be enrolled if they have received definitive treatment for symptom resolution. History of inflammatory process within 6 months prior to start of study treatment including but not limited to active peptic ulcer disease, diverticulitis or colitis. Significant traumatic injury within 4 weeks prior to start of study treatment. Uncontrolled pleural effusion or pericardial effusion requiring frequent drainage procedures (> once monthly). Patients with indwelling catheters (e.g. PleurX®) are allowed. History of nephrotic or nephritic syndrome. Uncontrolled hypertension defined as systolic pressure  Patients with untreated/uncontrolled CNS/leptomeningeal disease. Note: Patients with asymptomatic, treated CNS disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy and the following criteria are met:  No evidence of interim progression between the completion of CNS-directed therapy and the start of study enrollment. No stereotactic radiation or whole-brain radiation within 28 days prior to randomization. No evidence of intracranial hemorrhage or spinal cord hemorrhage.  Patients with active autoimmune disease requiring systemic corticosteroids greater than the equivalent of prednisone 10 mg daily or other systemic immunosuppressive medications including but not limited to: systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, colitis, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Bell's palsy, Guillain-Barré syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis, with the following exceptions:  Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone are eligible. Patients with controlled Type 1 diabetes mellitus on a stable insulin regimen are eligible. Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only are eligible provided: 1) rash covers < 10% of body surface area (BSA), 2) disease is well controlled at baseline and requires only low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, flucinolone 0.01%, desonide 0.05%, aclometasone dipropionate 0.05%).  Patients receiving treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor [TNF] agents) within 6 weeks must discontinue these medications prior to starting protocol therapy, with the exception of:  Patients with active autoimmune disease managed with systemic corticosteroids less than the equivalent of prednisone 10 mg daily. Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea). The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension and adrenocortical insufficiency. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan. Note: History of radiation pneumonitis in the radiation field (fibrosis) is permitted. Patients who have undergone prior solid organ or bone marrow transplant with the exception of patients with prior renal transplant for whom dialysis may be employed in the event of graft rejection. Patients with serious active infection within 2 weeks prior to enrollment (e.g. requiring hospitalization and/or intravenous [IV] antibiotics) infection within 2 weeks prior to enrollment, or currently receiving oral or IV antibiotics for the treatment of infection. Patients receiving prophylactic antibiotics are eligible.  Patients must have documented hepatitis virology status.  Patients with active hepatitis B virus (HBV) infection must have a viral load < 500 IU/mL within 28 days prior to start of study treatment and be on suppressive therapy (per local standard of care) for a minimum of 14 days prior to start of study treatment and for the length of the study. Patients with co-infection with HBV and hepatitis C virus (HCV) are excluded. Patients with a history of HCV infection but with negative HCV RNA by PCR are considered non-infected with HCV.  Patients with known human immunodeficiency virus (HIV) are allowed on study provided they have:  A stable regimen of highly active anti-retroviral therapy (HAART) No requirement for concurrent concurrent antibiotics or antifungal agents for the prevention of opportunistic infection A CD4 count above 250 cells/mcL An undetectable HIV viral load on standard PCR-based testing Patients with uncontrolled intercurrent illness (e.g., including but not limited to uncontrolled HTN [systolic BP ≥ 150, diastolic BP ≥ 100 despite optimal medical management or history of hypertensive crisis or hypertensive encephalopathy], symptomatic congestive heart failure [CHF], uncontrolled cardiac arrhythmia, or other within 3 months prior to start of study treatment or psychiatric illness/social situations or other conditions that would limit compliance with study requirements or substantially increase risk of incurring AEs in the opinion of the treating investigator. Patients with known concurrent malignancy that is expected to require active treatment within two years or may interfere with the interpretation of the efficacy and safety outcomes of this study in the opinion of the treating investigator. Note: Superficial bladder cancer, nonmelanoma skin cancers, and low-grade prostate cancer not requiring cytotoxic therapy should not exclude participation in this trial. Patients with CLL may be enrolled if they do not require active chemotherapy and their hematologic, renal and hepatic function meets criteria previously mentioned. Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of an investigational drug, may affect the interpretation of the results, or may render the patient at high risk from treatment complications in the opinion of the treating investigator. Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment. History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins or know hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab or bevacizumab infusion.