Novel microgels, microparticles and related polymeric materials capable of delivering bioactive materials to cells for use as vaccines or therapeutic agents. The materials are made using a crosslinker molecule that contains a linkage cleavable under mild acidic conditions. The crosslinker molecule is exemplified by a bisacryloyl acetal crosslinker. The new materials have the common characteristic of being able to degrade by acid hydrolysis under conditions commonly found within the endosomal or lysosomal compartments of cells thereby releasing their payload within the cell. The materials can also be used for the delivery of therapeutics to the acidic regions of tumors and sites of inflammation.