Microcavity polaritons are light-matter quasiparticles that arise from the strong coupling between excitons and photons confined in a semiconductor microcavity. They are typically studied at visible or near visible wavelengths. They combine the properties of confined electromagnetic fields, including a sizeable spin-orbit coupling, and the sensitivity to external magnetic fields and particle interactions inherited from their partly matter nature. These features make polaritons an excellent platform to study topological phases in photonics in one and two-dimensional lattices, whose band properties can be directly accessed using standard optical tools. In this review, we describe the main properties of microcavity polaritons and the main observations in the field of topological photonics, which include, among others, lasing in topological edge states, the implementation of a polariton Chern insulator under an external magnetic field, and the direct measurement of fundamental quantities, such as the quantum geometric tensor and winding numbers in one- and two-dimensional lattices. Polariton interactions open exciting perspectives for the study of nonlinear topological phases.