In this talk, I will introduce one of my research areas in the field of soft matter physics: topological defects in condensed matters. Topological defects originate from the broken continuous symmetry in phase transition, and they are mathematical singularities in the resulting ordered phases. Examples include dislocations and disclinations in crystals. Topological defects are fascinating objects permeating in fields as diverse as materials science, granular physics, biology and seismology. For example, the proliferation of dislocations has a strong connection with the plastic deformation and failure of materials, as well as the occurrence of earthquakes. In the field of soft matter physics, topological defects are crucial for understanding the open question of how various ordered structures are spontaneously formed. Much has been learned about the nature of topological defects by studying two-dimensional curved crystals; the curvature of the substrate will frustrate the otherwise perfect crystalline order. In this talk, I will introduce the concept of topological defects, and present our systematic researches on topological defects in both curved and planar two-dimensional crystals.