Bispecific antibodies usually do not occur in nature but are constructed by recombinant DNA or cell-fusion technologies. Most are designed to recruit cytotoxic effector cells of the immune system effectively against pathogenic target cells. This complex task explains why, after more than 15 years of extensive research, many different formats of bispecific antibodies have been developed but only a few have advanced to clinical trials. Here, we give a brief history of bispecific antibodies and review very recent progress towards formats that are beginning to solve the major issues of earlier formats. These improved bispecific antibodies are expected to show clinical efficacy in patients with cancer and other diseases, in a way that monoclonal antibodies have shown in recent years.