Study to Evaluate Adverse Events and Change in Disease Activity in Adult Participants With B-Cell Malignancies Receiving Oral ABBV-525 Tablets

B-cell malignancies are a group of cancers of B lymphocytes, a type of white blood cell responsible for fighting infections. The purpose of this study is to assess safety, tolerability, pharmacokinetics and preliminary efficacy of ABBV-525 as a monotherapy. ABBV-525 is an investigational drug being developed for the treatment of B-Cell Malignancies. Study doctors put the participants in groups called treatment arms. Participants will receive ABBV-525 at different doses. Approximately 150 adult participants will be enrolled in the study across sites worldwide. In part 1 (dose escalation), participants will receive escalating oral doses of ABBV-525. In part 2 (dose optimization), participants will receive one of two oral doses of ABBV-525, until the recommended phase 2 dose (RP2D) is determined. In part 3 (dose expansion), participants will receive the RP2D oral dose of ABBV-525. The estimated duration of the study is up to 64 months. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic and may require frequent medical assessments, blood tests, and scans.

Inclusion Criteria: * Dose Escalation (Part 1) Only: Participants with a documented diagnosis of one of the following third line or later of treatment (3L)+ mature B-cell malignancies, from the World Health Organization (WHO)-defined histologies as defined in the protocol. * Dose Optimization (Part 2) Only: Participants with documented diagnosis of chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) with histology based on WHO criteria, with measurable disease requiring treatment as defined by the International Workshop on Chronic Lymphocytic Leukemia (iwCLL). * Dose Expansion (Part 3) Only: Participants with documented diagnosis of one of the 3L+ mature B-cell malignancies based on WHO criteria listed in the protocol, with measurable disease requiring treatment. * Participant has an Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0, 1, or 2. * Participant has a life expectancy \>= 12 weeks. * Adequate hematological and hepatic function as defined in the protocol. * Must have archival or freshly collected tumor tissue for correlative studies before study enrollment. * Participants with prior central nervous system (CNS) disease that has been effectively treated may be eligible. * Participants with resolved coronavirus disease 2019 (COVID-19) infection are eligible. Exclusion Criteria: * Known active CNS disease, or primary CNS lymphoma. * Known bleeding disorders. * Known history of stroke or intracranial hemorrhage within 12 months prior to first dose of study treatment. * Uncontrolled active systemic infection, or active cytomegalovirus infection. * Active and/or chronic hepatitis B or C infection and/or the criteria listed in the protocol. * Known history of human immunodeficiency virus (HIV). * Known active COVID-19 infection. Participant must not have signs/symptoms associated with COVID-19 infection or known exposure to a confirmed case of COVID-19 infection during screening. If participant has signs/symptoms suggestive of COVID-19 infection, the participant must have a negative molecular (e.g., polymerase chain reaction) test or 3 negative antigen test results at least 24 hours apart.