In this lecture I give an overview of some of the classical results on the regularity of solutions to Navier-Stokes Equation. The overview includes the works of Serrin, Fabes-Jones-Riviere, Caffarelli-Kohn-Nirenberg, Constantin-Fefferman and Seregin-Sverak. I also explain how regularity questions for the flows of diffusions can be used to study Navier-Stokes Equation.