Currently, there is increasing interest in analysing brain activity in resting state, or under relatively natural conditions such as while watching a movie. When using functional magnetic resonance imaging (fMRI), such analysis is typically done by independent component analysis (ICA). However, there has not been very much work on analysing data measured by EEG or MEG in similar conditions. We have been recently developing various probabilistic methods for that purpose. First, we have created new variants of ICA to more effectively separate sources of brain activity by exploiting the special structure of EEG/MEG data. Second, we have developed tests of the statistical significance of the independent components. Third, we have a developed a framework for analysis of causality (connectivity) which uses the non-Gaussianity of the data in the context of Bayesian networks or structural equation models. In this talk, I will give a short introduction to the theory of ICA, and then I will discuss these recent developments.