Polymer nanoparticles offer significant benefits for improving delivery of biological therapeutics such as DNA and proteins, as they allow the cargo to be protected until it is delivered to a target cell. However, there are still challenges with achieving efficient delivery to the optimal cellular region. One significant roadblock is escape of nanoparticles from within the endosomal/lysosomal compartments into the cytosol. Here, we review the recent advances in understanding endosomal escape of polymer nanoparticles. We also discuss the current progress on investigating how nanoparticle structure can control endosomal escape. It is important to understand the fundamental biological processes that govern endosomal escape in order to design more effective therapeutic delivery systems.