Since the pioneering works by Leray in the 1930s, various sufficient conditions have been established for global regularity of the 3D Navier-Stokes equations. These criteria often require some smallness condition or symmetry structure of the initial condition. We are motivated by approximation perspective: is it possible to infer global regularity from one approximate solution, for instance from the size of a numerical solution? By assuming a relatively simple scale-invariant relation of the size of the approximate solution, the resolution parameter, and the initial energy, we show that the answer is affirmative for quite a general class of approximate solutions, including Leray's mollified solutions. In this talk, I will explain two methods (called global and local pictures) that lead to essentially the same result. Joint work with Vladimir Sverak.