The present invention provides antibodies that bind to prostate-specific membrane antigen (PSMA), bispecific antibodies that bind to PSMA and CD3, and methods of using the same. According to certain embodiments, the antibodies of the invention bind human PSMA with high affinity and bind CD3 to induce human T cell proliferation. The invention includes antibodies that bind PSMA and CD3 and induce T cell-mediated killing of PSMA-expressing tumor cells. According to certain embodiments, the present invention provides bispecific antigen-binding molecules comprising a first antigen-binding domain that specifically binds human CD3, and a second antigen-binding molecule that specifically binds human PSMA. In certain embodiments, the bispecific antigen-binding molecules of the present invention are capable of inhibiting the growth of prostate tumors expressing PSMA. The antibodies and bispecific antigen-binding molecules of the invention are useful for the treatment of diseases and disorders in which an upregulated or induced targeted immune response is desired and/or therapeutically beneficial. For example, the antibodies of the invention are useful for the treatment of various cancers.