Inclusion Criteria:  Histologically confirmed classical Hodgkin lymphoma Patients must be 12 years of age or older  Patients must have received at least 1-2 prior multi-agent chemotherapy or immunotherapy regimens will be divided into two cohorts based on the following clinical scenarios:  Patients enrolled to cohort A must have received only ONE prior brentuximab-containing regimen with NO prior checkpoint inhibitors. Patients enrolled to cohort A must have received brentuximab as part of their first-line treatment regimen. Patients enrolled to cohort B must have received only ONE prior immune checkpoint inhibitor- (i.e. nivolumab or pembrolizumab) containing regimen and NO prior brentuximab. Patients in cohort B may have received an immune checkpoint inhibitor during either their first- or second-line treatment regimen. If radiation is used as part of the planned front-line treatment regimen (i.e., brentuximab vedotin-doxorubicin-vinblastine-dacarbazine [BV-AVD] + radiation therapy [RT] for bulky stage II disease), this will count as only 1 prior therapy. Additionally, radiation as consolidation after a second-line multi-agent chemotherapy regimen is permitted and will not be counted as a third regimen No prior autologous or allogeneic transplant Eastern Cooperative Oncology Group (ECOG) performance status =< 2 for patients > 18 years old, or Lansky performance status of >= 50 for patients ages 12-18 years Enrolling patients must have measurable disease defined as a tumor or nodal mass > 1.5 cm in at least one dimension Resolution of all prior toxicities, including peripheral neuropathy, to a =< grade 1 Absolute neutrophil count (ANC) >= 750, unless disease related (within 28 days of cycle 1 day 1) Platelets >= 50,000, unless disease related (within 28 days of cycle 1 day 1) Creatinine =< upper limit of normal (ULN) (within 28 days of cycle 1 day 1) Aspartate aminotransferase/alanine aminotransferase (AST/ALT) =< 3 x ULN (within 28 days of cycle 1 day 1) Bilirubin =< 2 mg/dL (within 28 days of cycle 1 day 1) Patients with human immunodeficiency virus (HIV) infection are eligible. Patients with HIV infection must meet the following criteria: No evidence of co-infection with hepatitis B or C; CD4+ count >= 400/mm; no evidence of resistant strains of HIV; on anti-HIV therapy with an HIV viral load < 50 copies HIV ribonucleic acid (RNA)/mL. Patients with HIV must have ongoing follow-up with an infectious disease specialist and must have been evaluated within 90 days of cycle 1 day 1. Females of child-bearing potential (FCBP) must have a negative urine pregnancy test prior to starting therapy. If the test is positive, pregnancy must be ruled out  FCBP and men treated or enrolled on this protocol must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry for the duration of study participation, and 6 months after completion of brentuximab and/or nivolumab administration. 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.  A female of childbearing potential (FCBP) is a post-menarcheal woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months Completion of all previous therapy (including surgery, radiotherapy, chemotherapy, immunotherapy, or investigational therapy) for the treatment of cancer >= 2 weeks before the start of study therapy Patients with 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 Willingness and ability of the subject to comply with scheduled visits, drug administration plan, protocol-specified laboratory tests, other study procedures, and study restrictions Evidence of a personally signed informed consent by patients >= 18 year old (YO) or parent or legally authorized representative (LAR) for patients 12-17 YO indicating that the subject is aware of the neoplastic nature of the disease and has been informed of the procedures to be followed, the experimental nature of the therapy, alternatives, potential risks and discomforts, potential benefits, and other pertinent aspects of study participation. Patients 12-17 will also be required to give assent to the process per institutional guidelines  Exclusion Criteria:  Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject has been disease free for >= 2 years or which will not limit survival to < 2 years Patients who have had chemotherapy or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events to =< grade 1 Active autoimmune disease or history of autoimmune disease such as hepatitis, hypophysitis, nephritis, interstitial lung disease, and colitis Active central nervous system (CNS) involvement with lymphoma Patients with hepatitis B (positive hepatitis B virus surface antigen [HBsAg] or hepatitis B virus core antibody [HBcAb]) and those with positive hepatitis C virus (HCV) antibodies are not permitted to enroll No active infection, or other active illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements