The Stokes phenomenon refers to the fact that the analytic continuation of asymptotic solutions to certain systems of linear ODEs of second order cannot preserve their asymptotic behaviour. In this talk, we will introduce this phenomenon by studying some examples. After that, we will investigate the geometry (meromorphic connections) and topology (Stokes local systems) behind it, and finally we will discuss the associated Riemann-Hilbert(-Birkhoff) correspondence that relates them.