Exact testing has nowadays widespread applications in many areas of applied statistics. Distributional deviations from standard underlying distributions, censoring, mixtures, robustness, small sample studies are examples where exact tests are needed. Several projects (e.g. „Aktion“ or „Aso“) have been conducted in financial heavy tailed data, cancer testing, reliability testing, homogeneity and scale testing, dependence testing. We study also theoretical aspects of exact testing, like asymptotic properties (e.g. asymptotical optimality in Bahadur sense, limiting distribution), relation to concepts of robustness or scalability.