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This report documents the program and the outcomes of Dagstuhl Seminar 14372 "Analysis of Algorithms Beyond the Worst Case". The theory of algorithms has traditionally focused on worst-case analysis. This focus has led to both a deep theory and many beautiful and useful algorithms. However, there are a number of important problems and algorithms for which worst-case analysis does not provide useful or empirically accurate results. This is due to the fact that worst-case inputs are often rather contrived and occur hardly ever in practical applications. Only in recent years a paradigm shift towards a more realistic and robust algorithmic theory has been initiated. The development of a more realistic theory hinges on finding models that measure the performance of an algorithm not only by its worst-case behavior but rather by its behavior on "typical" inputs. In this seminar, we discussed various recent theoretical models and results that go beyond worst-case analysis. The seminar helped to consolidate the research and to foster collaborations among the researchers working in the different branches of analysis of algorithms beyond the worst case.