There is an increasing interest in the study of topological phases and topological band structures in the platforms of atomic, molecular, and optical physics (AMO physics), motivated both from the exploration of fundamental science and possibility for practical applications. This paper is intended to explain this exciting field assuming only basic knowledge on quantum mechanics and solid-state physics. After introducing atomic and optical settings where tight-binding lattice models can be realized, we explain basics of topological band structure, focusing on Chern insulators. We then explain how Chern insulators can be realized in the settings of AMO physics, concluding with unique topological phenomena that can be seen in AMO platforms.