Inclusion Criteria:  Patients must have:  A diagnosis of HLRCC with a histologic or cytologic confirmation of RCC consistent with this diagnosis (Cohort 1) OR Cytologically or histologically confirmed sporadic/non-HLRCC papillary renal cell carcinoma (Cohort 2) Patients must have advanced RCC with measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) by chest x-ray or as >= 10 mm (>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam. To be considered pathologically enlarged and measurable, a lymph node must be >= 15 mm (>= 1.5 cm) in short axis Patients must have received no more than two prior regimens targeting the VEGF pathway and no prior bevacizumab therapy in the metastatic/advanced setting. No prior treatment with PD-1 or PD-L1 inhibitors in the metastatic/advanced setting. No prior therapy is required for eligibility Age >= 12 years Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%) Absolute neutrophil count >= 1,000/mcL Platelets >= 100,000/mcL Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (< 3 x upper limit of reference range in patients with known/suspected Gilbert's disease) Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional ULN (or =< 5 x upper limit of reference range if considered to be related to liver or bone metastases by the principal investigator [PI])  Alkaline phosphatase =< 2.5 x institutional ULN (or =< 5 x upper limit of reference range if considered to be related to liver or bone metastases by the PI)  Note: For pediatric patients (< 18 years of age), ULN for alkaline phosphatase will be defined as 390 IU/L for males and 320 IU/L for females  Glomerular filtration rate (GFR) >= 30 mL/min/1.73 m^2  Note: For pediatric patients (< 18 years of age) the following creatinine thresholds will be utilized. Patients with a creatinine that exceeds this threshold will require further testing with a confirmation of GFR >= 40 as determined by either 24-hour urine collection or with radioisotope based nuclear medicine evaluation Age: 12 to < 13 years; Maximum serum creatinine (mg/dL): 1.2 (male); 1.2 (female) Age: 13 to < 16 years; Maximum serum creatinine (mg/dL): 1.5 (male); 1.4 (female)  Age: 16 to < 18 years; Maximum serum creatinine (mg/dL): 1.7 (male); 1.4 (female)  The threshold creatinine values in this table were derived from the Schwartz formula for estimating GFR, utilizing child length and stature data published by the Centers for Disease Control and Prevention (CDC) Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with an undetectable viral load within 6 months are eligible for this trial For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression/recurrence for >= 3 months and the patient no longer requires more than a physiologic dose of steroids Patients with a prior or concurrent invasive malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial Patients with a known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better The effects of study drugs on the developing human fetus are unknown. For this reason, all women and men of childbearing potential must agree to use adequate contraception (including but not limited to abstinence, barrier methods, hormonal contraceptives [birth control pills, injections, or implants], intrauterine device [IUD], tubal ligation, vasectomy) prior to study entry and for 6 months after completion of study therapy. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, and 6 months after completion of study drugs administration Subjects must provide archival tissue block or unstained tumor tissue or be willing to undergo biopsy to collect samples for retrospective central pathology review The ability of subject or parent/guardian to understand and the willingness to sign a written informed consent document or subjects with impaired decision making capacity (IDMC) if they are represented by a legally authorized representative (LAR)  Exclusion Criteria:  Patients who have had chemotherapy, radiotherapy, or major surgery within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to cycle 1, day 1. Surgical wounds must be healed prior to starting therapy. However, the following therapies are allowed:  Hormone-replacement therapy or oral contraceptives Herbal therapy > 1 week prior to cycle 1, day 1. All herbal therapy must be discontinued at least 1 week prior to cycle 1, day 1 Palliative radiotherapy for bone metastases > 2 weeks prior to cycle 1, day 1 Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities > grade 1 of the Common Terminology Criteria for Adverse Events [CTCAE] version [v]5 or to a level permitted under other sections of inclusion/exclusion criteria) with the exception of alopecia or electrolyte abnormalities that can be corrected to =< grade 1 prior to treatment initiation Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1 Treatment with systemic immunostimulatory agents (including, but not limited to, interferon [IFN]-alpha or interleukin [IL]-2) within 6 weeks prior to cycle 1, day 1  Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor [anti-TNF] agents) within 2 weeks prior to cycle 1, day 1  Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea or for purposes of pre-medication prior to radiology studies) may be enrolled The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed Hypercalcemia > grade 1 of the CTCAE v5 that is not corrected prior to treatment initiation Patients taking bisphosphonate therapy for symptomatic hypercalcemia. Use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed  History of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis  Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible  Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:  Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations Rash must cover less than 10% of body surface area (BSA) The disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%) No acute exacerbations of the underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids) History of idiopathic pulmonary fibrosis, pneumonitis (including drug-induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted Patients with active tuberculosis (TB) are excluded Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia  Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab  NOTE: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines and are not allowed. Influenza vaccination should be given during influenza season only (approximately October to March) Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring intravenous antibiotics, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements Poorly controlled hypertension with at least 2 occasions of elevated blood pressure within a week before treatment initiation (Adults: resting systolic blood pressure greater than 140 mmHg or diastolic blood pressure greater than 90 mmHg. Pediatric [< 18 years old]: Blood pressure [BP] >= the 95th percentile for age, height, and gender on at least two occasions separated by a 24-hour period despite optimal medical management) Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation History of anaphylactic or severe allergic reactions attributed to compounds of similar chemical or biologic composition to the study agents Patients with myocardial infarction, gastrointestinal (GI) perforation/fistula, intraabdominal abscess, or cerebrovascular accidents within 6 months before cycle 1, day 1 Documented baseline proteinuria > 1000 mg/day on 24-hour urine collection. Only patients with 1+ or greater proteinuria on urinalysis (UA) and a spot urine protein:creatinine ratio of > 0.5 will undergo a 24-hour urine collection for quantitation of proteinuria Pregnant women are excluded from this study because study drugs may have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study drugs, breastfeeding should be discontinued if the mother is treated with study drugs Serious, non-healing wound or ulcer; bone fracture within 3 months prior to treatment initiation Concomitant therapy with potent inhibitors of CYP450 3A4 (e.g. ketoconazole, verapamil, etc.) or potent CYP3A4 inducers or with potent CYP450 1A2 inhibitors (fluoroquinolone antibiotics including ciprofloxacin, levofloxacin, and norfloxacin; ticlodipine, cimetidine, amiodarone, etc.) who cannot discontinue or change these medications prior to the start of study treatment Patients who use tobacco or nicotine products and cannot stop their use of these products for the duration of study treatment