The present invention relates to antibodies, e.g., full length antibodies or antigen binding fragments thereof, that specifically bind to BCMA (B-Cell Maturation Antigen) and/or CD3 (Cluster of Differentiation 3). The invention also relates to antibody conjugates (e.g., antibody-drug-conjugates) comprising the BCMA antibodies, compositions comprising the BCMA antibodies, and methods of using the BCMA antibodies and their conjugates for treating conditions associated with cells expressing BCMA (e.g., cancer or autoimmune disease). The invention further relates to heteromultimeric antibodies that specifically bind to CD3 and a tumor cell antigen, (e.g., bispecific antibodies that specifically bind to CD3 and BCMA). Compositions comprising such heteromultimeric antibodies, methods for producing and purifying such heterodimeric antibodies, and their use in diagnostics and therapeutics are also provided.