Independent component analysis (ICA) aims at extracting unknown hidden factors/components from multivariate data using only the assumption that the unknown factors are mutually independent. Since the introduction of ICA concepts in the early 1980s in the context of neural networks and array signal processing, many new successful algorithms have been proposed that are now well-established methods. Since then, diverse applications in telecommunications, biomedical data analysis, feature extraction, speech separation, time-series analysis and data mining have been reported. Recently, exciting developments have moved the field towards more general source separation paradigms. In order to discuss these new directions, we organized a workshop with the title “ICA and beyond” as part of the “Neural Information Processing Systems” (NIPS) conference 2002 in Vancouver, Canada. This workshop was able to bring together an active community of researchers from various fields such as signal processing, machine learning, statistics and applications. Besides presenting the state of the art, open problems were also raised such as: what are the good applications for nonlinear blind source separation? Of high relevance especially for practitioners is the question whether estimated ICA components are meaningful or not, i.e. how can we assess the reliability of the ICA solution. Another direction is algorithms that cannot only identify one-dimensional ICA components but also multi-dimensional components like independent subspaces (dependent component analysis). Furthermore, new criteria and models based on Bayesian statistics have been presented. This special section of the Signal Processing journal summarizes the workshop and makes these new developments and questions available to a broader audience by including a peer-reviewed selection of 7 papers which were presented at the workshop. Following is a summary of those contributions. Three easy ways for separating nonlinear mixtures?