  The review presents general methods for treating complicated problems that
cannot be solved exactly and whose solution encounters two major difficulties.
First, there are no small parameters allowing for the safe use of perturbation
theory in powers of these parameters, and even when small parameters exist, the
related perturbative series are strongly divergent. Second, such perturbative
series in powers of these parameters are rather short, so that the standard
resummation techniques either yield bad approximations or are not applicable at
all. The emphasis in the review is on the methods advanced and developed by the
author. One of the general methods is {\it Optimized Perturbation Theory} now
widely employed in various branches of physics, chemistry, and applied
mathematics. The other powerful method is {\it Self-Similar Approximation
Theory} allowing for quite simple and accurate summation of divergent series.
These theories share many common features with the method of renormalization
group, which is briefly sketched in order to stress the similarities in their
ideas and their mutual interconnection.
