With the current biotherapeutic market dominated by antibody molecules, bispecific antibodies represent a key component of the next-generation of antibody therapy. Bispecific antibodies can target two different antigens at the same time, such as simultaneously binding tumor cell receptors and recruiting cytotoxic immune cells. Structural diversity has been fast-growing in the bispecific antibody field, creating a plethora of novel bispecific antibody scaffolds, which provide great functional variety. Two common formats of bispecific antibodies on the market are the single-chain variable fragment (scFv)-based (no Fc fragment) antibody and the full-length IgG-like asymmetric antibody. Unlike the conventional monoclonal antibodies, great production challenges with respect to the quantity, quality, and stability of bispecific antibodies have hampered their wider clinical application and acceptance. In this review, we focus on these two major bispecific types and describe recent advances in the design, production, and quality of these molecules, which will enable this important class of biologics to reach their therapeutic potential.