Intracellular nucleic acid delivery has the potential to treat many genetically-based diseases, however, gene delivery safety and efficacy remains a challenging obstacle. One promising approach is the use of polymers to form polymeric nanoparticles with nucleic acids that have led to exciting advances in non-viral gene delivery. Understanding the successes and failures of gene delivery polymers and structures is the key to engineering optimal polymers for gene delivery in the future. This article discusses the polymer structural features that enable effective intracellular delivery of DNA and RNA, including protection of nucleic acid cargo, cellular uptake, endosomal escape, vector unpacking, and delivery to the intracellular site of activity. The chemical properties that aid in each step of intracellular nucleic acid delivery are described and specific structures of note are highlighted. Understanding the chemical design parameters of polymeric nucleic acid delivery nanoparticles is important to achieving the goal of safe and effective non-viral genetic nanomedicine.