Drug-delivery systems are described which can serve as platforms for topical delivery of a variety of active pharmaceutical ingredients (API) to the surface of a mammalian body. Methods for the preparation and use of the compositions are also described. In some embodiments, the disclosed topical formulations include an API, a penetration enhancer/cosolvent, a gelling agent, and a neutralizing agent (to adjust pH). As compared to prior compositions, the disclosed topical formulations use a relatively small number of safe components and are easy to prepare with a high yield of finished product.