To overcome the skin's barrier properties that block transdermal delivery of most drugs, arrays of microscopic needles have been microfabricated primarily out of silicon or metal. This study addresses microneedles made of biocompatible and biodegradable polymers, which are expected to improve safety and manufacturability. To make biodegradable polymer microneedles with sharp tips, micro-electromechanical masking and etching were adapted to produce beveled- and chisel-tip microneedles and a new fabrication method was developed to produce tapered-cone microneedles using an in situ lens-based lithographic approach. To replicate microfabricated master structures, PDMS micromolds were generated and a novel vacuum-based method was developed to fill the molds with polylactic acid, polyglycolic acid, and their co-polymers. Mechanical testing of the resulting needles measured the force at which needles broke during axial loading and found that this failure force increased with Young's modulus of the material and needle base diameter and decreased with needle length. Failure forces were generally much larger than the forces needed to insert microneedles into skin, indicating that biodegradable polymers can have satisfactory mechanical properties for microneedles. Finally, arrays of polymer microneedles were shown to increase permeability of human cadaver skin to a low-molecular weight tracer, calcein, and a macromolecular protein, bovine serum albumin, by up to three orders of magnitude. Altogether, these results indicate that biodegradable polymer microneedles can be fabricated with an appropriate geometry and sufficient strength to insert into skin, and thereby dramatically increase transdermal transport of molecules.