Provided herein are antibodies which bind to latency-associated peptide (LAP) of TGF-β1 and are characterized by particular functional features, such as binding specifically to LAP-TGFβ1 on cells but not to LAP-TGFβ1 in extracellular matrix, as well as compositions including the same. Also provided are uses of these antibodies in therapeutic applications, such as in the treatment of cancer, and diagnostic applications.