Chemical reactions can be confined to nanoscale compartments by encapsulating catalysts in hollow nanoobjects. Such reaction compartments effectively become nanoreactors when substrate and product are exchanged between bulk solution and cavity. A key issue, thereby, is control of shell permeability. Nanoreactors exhibit selectivity and responsiveness if their shells discriminate among molecules and if access can be modulated by external triggers. Here, we review natural nanoreactors that include protein-based bacterial microcompartments, protein cages, and viruses. Artificial nanoreactors based on dendrimers, layer-by-layer capsules, and amphiphilic block copolymer polymersomes are also discussed. Selectivity in these nanoreactors is either due to intrinsic reactor-shell semipermeability or can be engineered using smart polymers to gate the reactors. Moreover, a rich repertoire of pores and channels are already provided in nature, e. g., in protein-based nanoreactors or in trans-membrane channel proteins. The latter can be reconstituted in polymersomes, resulting in gated vesicles. Nanoreactors hold promise for applications ranging from selective and size-constrained organic synthesis to biomedical advances (e.g., artificial organelles, biosensing) and as analytical tools to study reaction mechanisms.