Renormalization and resummation in field theories

Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions to problems of this type in static resummation. One is the use of auxiliary finite temperature UV divergent counterterms. The other is to use a renormalization scheme fitted to the environment. We also suggest a way how one could proceed in case of dynamic resummations.