Methods are provided for purifying peptides and proteins by incorporating the peptide or protein into a diketopiperazine or competitive complexing agent to facilitate removal of one or more impurities from the peptide or protein. Formulations and methods also are provided for the improved transport of active agents across biological membranes, resulting for example in a rapid increase in blood agent concentration. The formulations include microparticles formed of (i) the active agent, which may be charged or neutral, and (ii) a transport enhancer that masks the charge of the agent and/or that forms hydrogen bonds with the target biological membrane in order to facilitate transport. In one embodiment insulin is administered via the pulmonary delivery of microparticles comprising fumaryl diketopiperazine and insulin in its biologically active form. This method of delivering insulin results in a rapid increase in blood insulin concentration that is comparable to the increase resulting from intravenous delivery.