Topological quantum materials are a class of compounds featuring electronic band structures, which are topologically distinct from common metals and insulators. These materials have emerged as exceptionally fertile ground for materials science research. The topologically nontrivial electronic structures of these materials support many interesting properties, ranging from the topologically protected states, manifesting as high mobility and spin-momentum locking, to various quantum Hall effects, axionic physics, and Majorana modes. In this article, we describe different topological matters, including topological insulators, Weyl semimetals, twisted graphene, and related two-dimensional Chern magnetic insulators, as well as their heterostructures. We focus on recent materials discoveries and experimental advancements of topological materials, and their heterostructures. Finally, we conclude with prospects for the discovery of additional topological materials for studying quantum processes, quasiparticles and their composites, as well as exploiting potential applications of these materials.