Provided herein are BCMA-binding molecules, including anti-BCMA antibodies and antigen-binding fragments thereof such as heavy chain variable (VH) regions and single-chain antibody fragments, and chimeric receptors comprising the anti-BCMA binding molecules such as chimeric antigen receptors (CARs). In some embodiments, the anti-BCMA antibodies or antigen-binding fragments thereof specifically bind to BCMA-1. Among the anti-BCMA antibodies are human antibodies, including those that compete for binding to BCMA with reference antibodies, such as a non-human reference antibody. Also provided are genetically engineered cells expressing the CARs or BCMA-binding molecules and uses thereof such as in adoptive cell therapy.