The present invention relates to antibodies and their antigen-binding fragments and to other molecules that are capable of immunospecifically binding to B7-H1 or PD-1. In some embodiments such molecules are additionally capable of modulating the ability of B7-H1 or B7-DC to bind to PD-1 or are capable of affecting the signaling activity of the B7-H1 or PD-1. The invention additionally concerns the uses of such molecules in the diagnosis and treatment of cancer and other diseases.