Inclusion Criteria:  Confirmed diagnosis of chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) as per International Workshop on CLL (iwCLL) 2018 criteria.17 Participants must have relapsed after at least one prior line of therapy and must currently require therapy by iwCLL 2018 criteria.17 For enrollment to Cohort A: participants must be covalent BTK and BCL-2 inhibitor naïve. Participants who have received prior therapy with a covalent BTK or BCL-2 inhibitor are not eligible, including but not limited to prior treatment with ibrutinib or acalabrutinib. For enrollment to Cohort B: participants must have had prior treatment with a BTK inhibitor or a BCL-2 inhibitor, but not both, and must not have experienced disease progression as defined by iwCLL criteria while receiving therapy. For enrollment to Cohort C: participants must have disease that progressed during therapy with a covalent BTK inhibitor, not including zanubrutinib. For retreatment in patients who had residual MRD positivity at end of cycle 15 restaging: disease that has now progressed according to iwCLL criteria. Please note these patients do NOT need to meet iwCLL criteria for treatment, just for disease progression For retreatment in patients who had BM uMRD at end of cycle 15 restaging: two consecutive positive PB MRD tests, with confirmed MRD positivity in BM. Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of zanubrutinib and venetoclax in participants < 18 years of age and CLL/SLL is extremely rare in this population, children are excluded from this study. ECOG performance status ≤ 2 (Karnofsky ≥ 60%, see Appendix A).  Participants must have adequate organ function as defined below:  Platelet count ≥ 20,000/mcL Total bilirubin ≤ 2 × institutional upper limit of normal (ULN) (unless due to controlled hemolysis, Gilbert's disease, or is of non-hepatic origin) AST (SGOT) and ALT (SGPT) ≤ 4 × institutional ULN Serum Creatinine ≤ 1.5 × institutional ULN, OR Calculated creatinine clearance ≥ 50 mL/min (as calculated by the Cockcroft-Gault formula) The effects of zanubrutinib or venetoclax on the developing human fetus are unknown. For this reason and because anti-cancer agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. 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, for the duration of study participation, and 4 months after completion of study agent administration. Ability to understand and the willingness to sign a written informed consent document. Ability to swallow and retain oral medication.  Exclusion Criteria:  Known Cys481X mutation. For enrollment to Cohort B: participants who have received prior treatment with both a BTK inhibitor and BCL-2 inhibitor. Participants who have had previous anti-cancer therapy (e.g., chemotherapy, radiotherapy, immunotherapy, biologic therapy, hormonal therapy, surgery, investigational agents, and/or tumor embolization) within 2 weeks of Cycle 1 Day 1 with the following exceptions: Hormonal therapy given in the adjuvant setting Corticosteroid therapy (prednisone or equivalent ≤ 20 mg daily) is allowed as clinically warranted as long as the dose is stabilized at least for 7 days prior to initial dosing. Topical, inhaled, intra-articular, or ophthalmologic corticosteroids are permitted Participants enrolling to Cohort C may remain on prior BTK inhibitor therapy up until 2 days prior to Cycle 1 Day 1 History of a prior allogeneic hematologic stem cell transplant. Participants with known central nervous system (CNS) involvement, because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Participants with no known history of CNS involvement are not required to undergo CT scan or lumbar puncture (LP) for trial eligibility unless the participant is symptomatic as judged by the treating investigator. Participants who are receiving any other investigational agents at the time of study entry.  History of other malignancies, with the following exceptions:  Malignancy treated with curative intent and with no known active disease present for ≥ 2 years before the first dose of study drug and felt to be at low risk for recurrence by treating physician Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease Adequately treated carcinoma in situ without evidence of disease Low-risk prostate cancer on active surveillance Participants who have been vaccinated with live, attenuated vaccines < 4 weeks prior to Cycle 1 Day 1. Recent infection requiring intravenous antibiotics completed ≤ 7 days before the first dose of study drug, or any uncontrolled active systemic infection. Known bleeding disorders (e.g. von Willebrand's disease) or hemophilia. History of stroke, intracranial hemorrhage, or recent major bleed within 6 months prior to study entry. Participants who require warfarin or other vitamin K antagonists for anticoagulation (other anticoagulants are allowed with approval from the overall principal investigator). Participants who are known at the time of study entry to require concomitant treatment with any medications or substances that are moderate or strong CYP3A inhibitors or inducers. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product.  Known history of human immunodeficiency virus (HIV), active hepatitis C virus (HCV), or hepatitis B virus (HBV).  History of allergic reactions attributed to compounds of similar chemical or biologic composition to zanubrutinib or venetoclax. Participants with psychiatric illness/social situations that would limit compliance with study requirements. Pregnant women are excluded from this study because zanubrutinib and venetoclax are anti-cancer agents with 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 zanubrutinib or venetoclax, breastfeeding should be discontinued if the mother is treated with zanubrutinib or venetoclax. Participants with malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction.  Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or Class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to study entry.  Any life-threatening illness, medical condition, or organ system dysfunction that, in the treating investigator's opinion, could compromise the participant's safety or the integrity of the trial. Active and/or ongoing autoimmune anemia and/or autoimmune thrombocytopenia