The Stokes phenomenon refers to the fact that the analytic continuation of asymptotic solutions to certain second-order linear ODEs cannot preserve the asymptotic behavior. In this talk, we will introduce this phenomenon by studying some examples. Then, we will investigate the geometry (meromorphic connections) and topology (Stokes local systems) behind it. Finally, we will illustrate an irregular nonabelian Hodge correspondence related to them. Based on a recent joint work with Hao Sun.