Microcavity exciton-polaritons are attractive quantum quasi-particles resulting from strong light-matter coupling in a quantum-well-cavity structure. They have become one of the most stimulating solid-state material platforms to explore beautiful collective quantum phenomena originating from macroscopic coherence in condensation and superfluidity, Berezinskii-Kosterlitz-Thouless transition, and various topological excitations in the form of solitons, vortices, and skyrmions. They can also provide opportunities for the development of pioneering photonic devices by exploiting bistability and parametric scatterings due to strong nonlinearity that possess remarkable performance advantages of power-efficient operation, ultrafast response time, and scalable planar geometries. This story becomes profound and fascinating when the spins of excitons are taken into account, that can be directly accessed through light polarization states. The purpose of this review is to give central principles of microcavity exciton-polariton spins and their anisotropic interactions, which can couple with the effective magnetic fields from mode-splitting of microcavity photons and spin-dependent relaxation processes of quantum-well excitons. Furthermore, notable theoretical and experimental research activities are summarized to reveal extraordinary quantum phenomena of spin-resolved topological states and exotic spin textures and to devise novel spin-based photonic devices based on microcavity exciton-polaritons.