• Diagnosis of:

‣ CLL with an indication for treatment based on the Investigator's opinion and measurable disease, or

⁃ SLL (lymphadenopathy and/or splenomegaly and \< 5×10\^9 CD19+ CD5+ clonal B lymphocytes/L \[\< 5000/µL\] in the peripheral blood at diagnosis with measurable disease that is biopsy-proven SLL)

• Subjects (other than those in the ibrutinib + JCAR017 combination therapy and DEME cohort) must have received and failed Bruton tyrosine kinase inhibitor (BTKi) treatment or have been deemed ineligible for BTKi therapy.

• Subjects in the JCAR017 monotherapy cohorts must have received previous treatment as follows:

‣ Monotherapy cohorts EXCEPT DEME cohort: Subjects with CLL or SLL and high-risk features must have failed at least 2 lines of prior therapy.

⁃ Monotherapy cohorts EXCEPT DEME cohort: Subjects with CLL or SLL and standard-risk features must have failed at least 3 lines of prior therapy.

⁃ DEME cohort ONLY: Subjects with relapsed or refractory CLL or SLL, irrespective of cytogenetic risk features, must have received at least 2 lines of prior therapy including a BTKi and a BCL2i.

• Subjects in the ibrutinib + JCAR017 combination therapy cohort must either:

‣ be receiving ibrutinib and progressing at the time of study enrollment

⁃ be receiving ibrutinib for at least 6 months with a response less than complete response/remission (CR) and have high-risk features as defined in inclusion criterion 5a

⁃ have BTK or PLCgamma2 mutations per local laboratory assessment, with or without progression on ibrutinib

⁃ have previously received ibrutinib and have no contraindications to restarting ibrutinib

• Eastern Cooperative Oncology Group performance status of ≤ 1

• Assessed by the Investigator to have adequate bone marrow function to receive lymphodepleting chemotherapy

• Adequate organ function, defined as:

‣ Serum creatinine ≤ 1.5 × age-adjusted upper limit of normal (ULN) OR calculated creatinine clearance \> 30 mL/min

⁃ Alanine aminotransferase ≤ 5 × ULN and total bilirubin \< 2.0 mg/dL (or \< 3.0 mg/dL for subjects with Gilbert's syndrome or leukemic infiltration of the liver)

⁃ Adequate pulmonary function, defined as ≤ Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 dyspnea and saturated oxygen (SaO2) ≥ 92% on room air

⁃ Adequate cardiac function, defined as left ventricular ejection fraction ≥ 40% as assessed by echocardiogram or multiple uptake gated acquisition scan performed within 30 days prior to determination of eligibility

• Subject either currently has central vascular access or is a candidate to receive central vascular access or peripheral vascular access for leukapheresis procedure.

• If prior CD19-targeted therapy has been administered, subject must have CD19-positive disease confirmed by immunohistochemistry or flow cytometry since completing the prior CD19-targeted therapy.

• Subjects in ibrutinib + JCAR017 combination cohort must have progressed on a BTKi and have received prior therapy with venetoclax

• Subjects in venetoclax + JCAR017 combination cohort must:

‣ have failed at least 1 prior line of therapy, including failed BTKi therapy or have been deemed ineligible to receive BTKi

⁃ be venetoclax naive (required for dose expansion) or

⁃ if prior venetoclax (only for dose escalation)

⁃ have no contraindictions to re-initiation of venetoclax based on prior intolerance and have had at least 6 months elapsed since the last dose of venetoclax, if either, best response was stable disease, or subject experienced disease progression on venetoclax, or within 6 months of venetoclax discontinuation

• subjects in the venetoclax + JCAR017 combination must have hemoglobin \>=9 g/dL, absolute neutrophil count \>=500mm3 and platelets\>= 75,000/mm3, unless cytopenias are judged by investigator to be due to CLL infiltration of the bone marrow

• must have diagnosis of CLL or SLL with an indication for treatment based on the investigator's opinion and measurable disease (any of the following measurable lymph nodes ≥1.5 cm in the greatest transverse diameter and/or hepatomegaly or splenomegaly) and demonstration of CLL cells in the peripheral blood by flow cytometry