In this talk, I will describe the definition of Gromov-Hausdorff (GH) convergence for metric spaces. Gromov's precompactness Theorem guarantees that any sequence of $n$-dimensional Riemannian manifolds with a Ricci curvature lower bound has a subsequence GH converging to a metric space, which we call a Ricci limit space. Then I will discuss Cheeger-Colding-Naber Theory about geometric structure of a Ricci limit space. Finally, I will show some topological results about Ricci limit spaces.