The incidence of non-Hodgkin lymphomas is on the rise worldwide. The aggressive non-Hodgkin lymphomas can potentially be cured with front-line therapy, but indolent ones, such as chronic lymphocytic leukemia/small lymphocytic lymphoma, cannot. Relapsed/refractory non-Hodgkin lymphomas have a poor overall outcome, typically with shorter responses after each relapse. Novel therapies are sought to improve outcomes in this patient population. This review discusses the promising new biologic therapies that have emerged over the last 5 years. Some have already achieved US Food and Drug Administration approval, while others are undergoing active investigation in order to ultimately gain approval. Here, in Part 1, we discuss monoclonal antibodies. In Part 2, we will discuss adoptive cellular immunotherapies, small-molecule inhibitors, and immunomodulatory agents.