Inclusion Criteria:  Participants must be aged ≥18 years at the time of screening. Written informed consent and any locally required authorization (e.g., Health Insurance Portability and accountability Act in the US, European Union (EU) data privacy regulations in the EU) obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations. Life expectancy ≥6 months. HCC, diagnosed by radiographic imaging or histology. Patient not a candidate for liver resection, thermal ablation, or transplantation at the time of study entry. Treatment naïve. Measurable disease by mRECIST criteria (e.g. ≥10mm of enhancement). Tumor volume ≤25% of whole liver volume (determined by imaging). Unilobar tumor Future liver remnant volume (FLRV) ≥30% of whole liver volume. FRLV is the volume of liver not planned to be treated with TheraSphere and free of HCC.  Patients with HBV or HCV infection are to have documented virology status of hepatitis as confirmed by HBV and HCV serology test:  Patients with HBV infection: HBV DNA load should be ≤2000 IU/mL obtained within 28 days prior to initiation of study treatment, and Anti-HBV treatment (per local standard of care; e.g., entecavir) for a minimum of 14 days prior to study entry and willingness to continue treatment for the length of the study Patients with chronic HCV infection are allowed in the study: for untreated patients, AST/ALT should be ≤3xULN and for treated patients, antiviral treatment (per local standard of care) should be stopped for a minimum of 14 days prior to study entry and AST/ALT should be ≤3xULN Patient with Human Immunodeficiency Virus (HIV) infection is eligible with well controlled HIV infection, no current or previous AIDS-related complications and CD4+ T-cell (CD4+) counts ≥ 350 cells/uL Negative serum pregnancy test in females of child-bearing potential; patients who are breast-feeding cannot participate in this trial. Adequate contraception for the patient and his/her sexual partner.  Adequate renal and marrow function as defined below:  Hemoglobin ≥9.0 g/dL Absolute neutrophil count ≥1.5 x 109/L Platelet count ≥75 x 109/L Measured or calculated creatinine clearance ≥45 mL/min as determined by Cockcroft-Gault (using actual body weight) Absolute lymphocyte count ≥1.0 X 109/L  Adequate liver function, as defined by  Child-Pugh A Serum albumin ≥30 g/L Serum bilirubin <1.1 x the upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome, who will be permitted to enroll in the study in consultation with their physician. AST and ALT <3 x ULN. Eastern Cooperative Oncology Group (ECOG) performance status of 0 at randomization. Body weight >30 kg and BMI ≥18 kg/m2.  Exclusion Criteria:  Any contraindication to angiography or selective visceral catheterization. Cone Beam CT (CBCT) or Technetium-99m macroaggregated Albumin (99mTc-MAA) hepatic arterial perfusion scintigraphy shows any deposition to the gastrointestinal tract that may not be corrected by angiographic techniques. CBCT or 99mTc-MAA hepatic arterial perfusion scintigraphy shows poor tumor targeting that would lead to a dose that does not meet the liver dosing criteria specified in section 9.1, if lobar administration with multi-compartment dosimetry is planned. Shunting of blood to the lungs that could result in delivery of >30 Gy to the lungs in a single treatment or >50 Gy cumulative dose to the lungs in case of multiple TheraSphere treatments, as seen on 99mTc-MAA hepatic arterial perfusion scintigraphy. Extrahepatic metastases, including patients with hilar /mesenteric /celiac lymph nodes >1.5 cm in shorter axis, or with lung nodules (single lesion, > 1 cm, or multiple smaller lesions with a total diameter >2 cm) Brain metastases, leptomeningeal carcinomatosis or spinal cord compression. Patients with suspected brain metastases at screening should have an MRI (preferred) or CT each preferably with IV contrast of the brain prior to study entry. . Evidence of any tumor vascular invasion. Any prior treatment for HCC including surgery, TACE/TAE, ablation, systemic, and/or radiation treatment (including radiation treatment to the liver for any diagnosis). Prior exposure to any immune mediated therapy, including but not limited to other anti PD-1, anti-PDL-1, anti-PDL2, anti-CTLA-4, antibodies, IFN. Concurrent treatment for HCC or treatment in the last 4 weeks in another clinical study, unless it is an observational study (non-interventional) or during a non-interventional follow-up stage of an interventional study, or prior randomization to this study Hepatic encephalopathy present at study entry and/or episodes of encephalopathy (≥Grade 2) within 6 months prior to randomization. Presence of ascites, clinical or radiological, "trace" of ascites is acceptable. HCC with infiltrative disease presentation that is not possible to evaluate by mRECIST. History of active primary/acquired immunodeficiency. Evidence of pulmonary insufficiency (defined by an arterial oxygen pressure (Pa,O2) of <60 mmHg, or oxygen saturation (Sa,O2) of <90% (Roussos & Koutsoukou, 2003) or clinically evident chronic obstructive pulmonary disease (COPD). Medical history of radiation pneumonitis or recent pneumonitis, regardless of causality History of any organ allograft, including bone marrow allo and autograft.  Active or prior documented autoimmune or inflammatory disorders (including but not limited to, inflammatory bowel disease [e.g. ulcerative colitis or Crohn's disease], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome [granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc]). The following are exceptions to this criterion:  Patients with vitiligo or alopecia Patients with hypothyroidism (e.g. following Hashimoto's syndrome) stable on hormone replacement therapy Any chronic skin condition that does not require systemic therapy. Patients without active disease in the last 5 years may be included but only after consultation with the Sponsor Study physician. Patients with celiac disease controlled by diet alone.  Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab. The following are exceptions to this criterion:  Intranasal, inhaled, topical steroids, or local steroid injections (e.g. intra-articular injection) Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent. Steroids as premedication for hypersensitivity reactions (e.g. CT scan premedication). History of gastrointestinal bleeding within 28 days prior to randomization, active GI bleeding and any bleeding diathesis or coagulopathy that is not correctable by usual therapy or hemostatic agents (e.g. closure device). Patients with known varices that have not bled can enter the study. No endoscopic exploration is required before randomization. Presence of biliary stent at any time or sphincterotomy within one year prior to randomization. History of malignancy, other than HCC, within three years, with the exception if adequately treated carcinoma in situ of the cervix, early squamous cell carcinoma or basal cell carcinoma of the skin , localized prostate cancer, ductal carcinoma in situ, or low grade endometrial carcinoma with no myometrial invasion (negligible risk of metastases or death 5-year OS rate >90%). Major surgical procedure (as defined by the Investigator) within 28 days prior to randomization. A history of severe allergy or intolerance to contrast agents, narcotics, sedatives or atropine that cannot be managed medically. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis testing in line with local practice), HBV and HVC co-infection, HBV and Hep D co-infection, or human immunodeficiency virus (HIV 1/2 antibodies) plus HCV or HBV co-infection. Receipt of live attenuated vaccine within 30 days prior to the first dose of durvalumab and/or tremelimumab. Note: patients, if enrolled, should not receive live vaccine whilst receiving durvalumab and/or tremelimumab and up to 30 days after the last dose of durvalumab and/or tremelimumab. Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab and tremelimumab monotherapy. Unstable chronic disease or evidence of any disease or condition that would place the patient at undue risk and preclude safe use of TheraSphere, durvalumab and tremelimumab treatment, including but not limited to, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, active interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent. Patient not able to follow the TheraSphere, durvalumab or tremelimumab treatment requirements.