Organic-inorganic perovskite solar cells have achieved an impressive power conversion efficiency of up to 25.6% and 24.8%, respectively, for single and multijunction tandem architectures due to the huge progress made in the rational design and development of both the perovskite absorbers and the charge transport and electrode materials used as the selective contacts. The interfaces between the perovskite film and the charge transport layers are among the most critical factors in determining the efficiency and stability of perovskite solar cells regardless of the structure employed (mesoporous (mp) or planar heterostructure). Herein, an overview is provided on the recent advances in the fundamental understanding of how these interfaces, upon incorporating various functional charge transport layers, influence the performance of mp perovskite solar cells (mp-PSCs) where the perovskite is deposited and embedded in a high porosity and surface area mp material. First, the most critical aspects of such materials that govern the performance of the complete device are discussed including the energy level alignment at the interfaces, charge transport in interfacial layers, defects in the perovskite, interfacial layers or at their interfaces, as they all strongly affect interfacial charge recombination and extraction. In this context, we will discuss the various strategies for the interfaces and the interfacial materials employed both for the hole (HTM) and electron (ETM) transport/extraction. Next, advances in the performance of a highly promising alternative mp architecture, namely HTM-free triple mp-PSCs, where the HTL is removed to reduce complexity and manufacturing cost for printable mp PSCs, will be discussed. Finally, an outlook for the development of highly efficient and stable mpPSCs will be provided.