This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic whyexplanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabilistic relevance, maximal specifity and homogenity, the height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both deductive and probabilistic explanations (...) are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models. (shrink)