Gene silencing via RNA interference (RNAi) is rapidly evolving as a personalized approach to cancer treatment. The effector molecules—small interfering RNAs (siRNAs) and microRNAs (miRNAs)—can be used to silence or “switch off” specific cancer genes. Currently, the main barrier to implementing siRNA- and miRNA-based therapies in clinical practice is the lack of an effective delivery system that can protect the RNA molecules from nuclease degradation, deliver to them to tumor tissue, and release them into the cytoplasm of the target cancer cells, all without inducing adverse effects. Here, we review the fundamentals of RNAi, cell membrane transport pathways, and factors that affect intracellular delivery. We discuss the advantages and disadvantages of the various types of nanoparticle delivery systems, with a focus on those that have been investigated in breast cancer in vivo.