The importance of an interplay between topology and symmetries has been recognized over years since the discoveries of time-reversal symmetric topological insulators. While initially the effects of non-spatial symmetry such as time-reversal symmetry have been focused, it has been becoming clear that spatial symmetries such as reflection symmetry and point group symmetries also give rise to interesting topological phases of matter, including “crystalline topological insulators”. More generally, symmetry-protected topological phases of matter, i.e., phases of matter that are not adiabatically connected to a trivial phase such as an atomic insulator once a symmetry condition is enforced, has been widely discussed. In this talk, I plan to overview recent developments in phases of matter with reflection symmetry (parity symmetry) with and without interactions. For non-interacting fermion systems, I will discuss a systematic classification of topological phases in a manner similar to the periodic table of topological insulators and superconductors (also known as “10-fold way”). I will also discuss how interactions modify the free fermion classification.