Chimeric antigen receptor (CAR) T-cell therapy is a promising immunotherapy based on genetically engineered T cells derived from patients. The introduction of CAR T-cell therapy has changed the treatment paradigm of patients with B-cell lymphoid malignancies. However, challenging issues including managing life-threatening toxicities related to CAR T-cell infusion and resistance to CAR T-cell therapy, leading to progression or relapse, remain. This review summarizes the issues with currently approved CAR T-cell therapies for patients with relapsed or refractory B-cell lymphoid malignancies, including lymphoma and myeloma. We focus on unique toxicities after CAR T-cell therapy, such as cytokine-related events and hematological toxicities, and the mechanisms underlying post-CAR T-cell failure.