Monoclonal antibodies have found wide applications in the treatment of cancer, as well as of autoimmune, infectious, and other diseases. Several dozen new antibodies are currently undergoing different stages of clinical trials, and some of them will soon be added to the list of immunotherapeutic drugs. Most of these antibodies have been generated using hybridoma technology or a phage display. In recent years, new methods of obtaining human monoclonal antibodies have been actively developing. These methods rely on sequencing immunoglobulin genes from B lymphocytes, as well as on the creation of antibody-secreting stable B-cell lines. The term next-generation antibody-discovery platforms has already been established in the literature to refer to these approaches. Our review focuses on describing the results obtained by these methods.