Parsing models have many applications in AI, ranging from natural language processing (NLP) and computational music analysis to logic programming and computational learning. Broadly conceived, a parsing model seeks to uncover the underlying structure of an input, that is, the various ways in which elements of the input combine to form phrases or constituents and how those phrases recursively combine to form a tree structure for the whole input. During the last fifteen years, a major shift has taken place from rule-based, deterministic parsing to corpus-based, probabilistic parsing. A quick glance over the NLP literature from the last ten years, for example, indicates that virtually all natural language parsing systems are currently probabilistic. The same development can be observed in (stochastic) logic programming and (statistical) relational learning. This trend towards probabilistic parsing is not surprising: the increasing availability of very large collections of text, music, images and the like allow for inducing statistically motivated parsing systems from actual data.