In this talk, we will discuss a standard blowing up procedure as applied to a space-time region near a possible singular point of a suitable weak solution. Suppose that we have a singularity of a suitable weak solution at the origin of the space-time, a blowing up procedure is essentially the same as the one which consists of a sequence of magnifications of the structure of the solution near the singular point at smaller and smaller temporal-spatial scales shrinking down to 0. Each time, the magnification will be done by means of the natural scaling of the time-dependent Navier-Stokes equation. The resulting product of this process of successive magnifications would yield a limiting profile which reflects the asymptotic structure of the singularity of the solution. We will see that the limiting profile would be special type of ancient bounded weak solution to the Navier-Stokes equation, which will be called ancient bounded mild solution.