The recent works on supported isolated metal atoms and metal clusters with a few atoms have reformed our understanding on the structure-reactivity relationship established on conventional nanoparticulate catalysts. One critical issue related to supported subnanometric metal catalysts (including both isolated atoms and clusters) on conventional open-structure carriers is the stability of the metal entities, since they may sinter into large nanoparticles under harsh reaction conditions. By confining the isolated metal atoms or subnanometric metal clusters in crystalline porous materials (such as zeolites and metal-organic frameworks) can improve the stability of these tiny species against sintering into nanoparticles. More importantly, the interaction between the metal species and the porous framework may modulate the geometric and electronic structures of the subnanometric metal species, especially in the cases of metal clusters. Such confinement effect can induce shape-selective catalysis or unique chemoselectivity compared to the counterpart metal entities supported on conventional open-structure solid carriers. In this review, we will discuss the structural features, synthesis methodologies, characterization techniques and catalytic applications of subnanometric species confined in zeolites and metal-organic frameworks, aiming to make critical comparison between confined and un-confined isolated atoms and metal clusters and to give perspectives on the future developments.