Provided are isolated nucleic acid molecules encoding chimeric antigen receptors (CARs) that bind to tumor antigens. Also provided are isolated polypeptides and CARs encoded by the isolated nucleic acid molecules, vectors that include the isolated nucleic acid molecules, cells that include the isolated nucleic acid molecules, methods of making the same, and methods for using the same to generate a persisting population of genetically engineered T cells in a subject, expanding a population of genetically engineered T cells in a subject, modulating the amount of cytokine secreted by a T cell, reducing the amount of activation-induced calcium influx into a T cell, providing an anti-tumor immunity to a subject, treating a mammal having a MUC1-associated disease or disorder, stimulating a T cell-mediated immune response to a target cell population or tissue in a subject, and imaging a MUC1-associated tumor.