Nucleic acids are a promising type of therapeutic for the treatment of a wide range of conditions, including cancer, but they also pose many delivery challenges. For efficient and safe delivery to cancer cells, nucleic acids must generally be packaged into a vehicle, such as a nanoparticle, that will allow them to be taken up by the target cells and then released in the appropriate cellular compartment to function. As with other types of therapeutics, delivery vehicles for nucleic acids must also be designed to avoid unwanted side effects; thus, the ability of such carriers to target their cargo to cancer cells is crucial. Classes of nucleic acids, hurdles that must be overcome for effective intracellular delivery, types of nonviral nanomaterials used as delivery vehicles, and the different strategies that can be employed to target nucleic acid delivery specifically to tumor cells are discussed. Additonally, nanoparticle designs that facilitate multiplexed delivery of combinations of nucleic acids are reviewed.