The ability to efficiently access cytosolic proteins is desired in both biological research and medicine. However, targeting intracellular proteins is often challenging, because to reach the cytosol, exogenous molecules must first traverse the cell membrane. This review provides a broad overview of how certain molecules are thought to cross this barrier, and what kinds of approaches are being made to enhance the intracellular delivery of those that are impermeable. We first discuss rules that govern the passive permeability of small molecules across the lipid membrane, and mechanisms of membrane transport that have evolved in nature for certain metabolites, peptides, and proteins. Then, we introduce design strategies that have emerged in the development of small molecules and peptides with improved permeability. Finally, intracellular delivery systems that have been engineered for protein payloads are surveyed. Viewpoints from varying disciplines have been brought together to provide a cohesive overview of how the membrane barrier is being overcome.