Chimeric antigen receptor-modified (CAR) T cells targeting CD19 have revolutionized the treatment of relapsed or refractory aggressive B-cell lymphomas, and their use has increased the cure rate for these cancers from 10 to 40%. Two second-generation anti-CD19 CAR T-cell products, axicabtagene ciloleucel and tisagenlecleucel, have been approved for use in patients, and the approval of a third product, lisocabtagene maraleucel, is expected in 2020. The commercial availability of the first two products has facilitated the development of real-world experience in treating relapsed or refractory aggressive B-cell lymphomas, shed light on anti-CD19 CAR T-cell products' feasibility in trial-ineligible patients, and raised the need for strategies to mitigate the adverse effects associated with anti-CD19 CAR T-cell therapy, such as cytokine release syndrome, neurotoxicity, and cytopenia. In addition, promising clinical data supporting the use of anti-CD19 CAR T-cell therapy in patients with indolent B-cell lymphomas or chronic lymphocytic leukemia have recently become available, breaking the paradigm that these conditions are not curable. Multiple clinical CAR T-cell therapy-based trials are ongoing. These include studies comparing CAR T-cell therapy to autologous stem cell transplantation or investigating their use at earlier stages of disease, novel combinations, and novel constructs. Here we provide a thorough review on the use of the anti-CD19 CAR T-cell products axicabtagene ciloleucel, tisagenlecleucel and lisocabtagene maraleucel in patients with indolent or aggressive B-cell lymphoma or with chronic lymphocytic leukemia, and present novel CAR T cell-based approaches currently under investigation in these disease settings.