The application of nanotechnology in the field of drug delivery has attracted much attention in the latest decades. Recent breakthroughs on the morphology control and surface functionalization of inorganic-based delivery vehicles, such as mesoporous silica nanoparticles (MSNs), have brought new possibilities to this burgeoning area of research. The ability to functionalize the surface of mesoporous-silica-based nanocarriers with stimuli-responsive groups, nanoparticles, polymers, and proteins that work as caps and gatekeepers for controlled release of various cargos is just one of the exciting results reported in the literature that highlights MSNs as a promising platform for various biotechnological and biomedical applications. This review focuses on the most recent progresses in the application of MSNs for intracellular drug delivery. The latest research on the pathways of entry into live mammalian and plant cells together with intracellular trafficking are described. One of the main areas of interest in this field is the development of site-specific drug delivery vehicles; the contribution of MSNs toward this topic is also summarized. In addition, the current research progress on the biocompatibility of this material in vitro and in vivo is discussed. Finally, the latest breakthroughs for intracellular controlled drug release using stimuli-responsive mesoporous-silica-based systems are described.