Key Inclusion Criteria:

          1. Participants must meet protocol defined disease criteria requiring treatment for their
             respective disease prior to initiation of ibrutinib or acalabrutinib

          2. Ibrutinib and acalabrutinib intolerance is defined as an unacceptable toxicity where,
             in the opinion of the investigator, treatment should be discontinued in spite of
             optimal supportive care as a result of one of the following:

               1. For ibrutinib and acalabrutinib intolerance events:

                    -  1 or more ≥ Grade 2 nonhematologic toxicities for >7 days (with or without
                       treatment)

                    -  1 or more ≥ Grade 3 nonhematologic toxicity of any duration

                    -  1 or more Grade 3 neutropenia with infection or fever of any duration; or

                    -  Grade 4 heme toxicity which persists to the point that the investigator
                       chose to stop therapy due to toxicity NOT progression.

               2. For acalabrutinib intolerance events only;

                    -  1 or more ≥ Grade 1 nonhematologic toxicities of any duration with > 3
                       recurrent episodes; or

                    -  1 or more ≥ Grade 1 nonhematologic toxicities for > 7 days (with or without
                       treatment); or

                    -  Inability to use acid-reducing agents or anticoagulants (eg, proton pump
                       inhibitors, warfarin) due to concurrent acalabrutinib use

          3. Ibrutinib and/or acalabrutinib-related ≥ Grade 2 toxicities must have resolved to ≤
             Grade 1 or baseline prior to initiating treatment with zanubrutinib. Grade 1
             acalabrutinib-related toxicities must have resolved to Grade 0 or baseline prior to
             initiating treatment with zanubrutinib.

          4. Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2

          5. Absolute neutrophil count (ANC) ≥ 1000/mm^3 with or without growth factor support and
             platelet count ≥ 50,000/mm^3 (may be post-transfusion), on or prior to C1D1 of
             zanubrutinib

        Key Exclusion Criteria:

          1. Clinically significant cardiovascular disease including the following:

               1. Myocardial infarction within 6 months before the Screening

               2. Unstable angina within 3 months before the Screening

               3. New York Heart Association class III or IV congestive heart failure

               4. History of sustained ventricular tachycardia, ventricular fibrillation, and/or
                  Torsades de Pointes

               5. QT interval corrected by Fridericia's formula > 480 milliseconds

               6. History of Mobitz II second-degree or third-degree heart block without a
                  permanent pacemaker in place

          2. History of central nervous system (CNS) hemorrhage

          3. Documented progressive disease (PD) during ibrutinib and/or acalabrutinib treatment.

          4. Have received any anticancer therapy (other than immunotherapy) for CLL/SLL, WM, MCL,
             and MZL < 7 days before any Screening assessments are performed or any immunotherapy
             treatment, taken alone or as part of a chemoimmunotherapy regimen, < 4 weeks before
             any Screening assessments are performed

          5. Requires ongoing need for corticosteroid treatment > 10 mg daily of prednisone or
             equivalent corticosteroid. Note: Systemic corticosteroids must be fully tapered
             off/discontinued ≥ 5 days before the first dose of study drug is administered.

        NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.