In the past, neural networks were viewed as classification and regression systems whose internal representations were incomprehensible. It is now becoming apparent that algorithms can be designed that extract comprehensible representations from trained neural networks, enabling them to be used for data mining and knowledge discovery, that is, the discovery and explanation of previously unknown relationships present in data. This chapter reviews existing algorithms for extracting comprehensible representations from neural networks and outlines research to generalize and extend the capabilities of one of these algorithms, TREPAN. This algorithm has been generalized for application to bioinformatics data sets, including the prediction of splice site junctions in human DNA sequences, and cheminformatics. The results generated on these data sets are compared with those generated by a conventional data mining technique (C5) and appropriate conclusions are drawn.