In this review, we mainly discuss the origin and the development of statistical learning research, as well as constraints and brain neural bases of statistical learning. Researches of statistical learning originated from the studies on speech segmentation in human infants since 1990's. From then on, lots of studies have explored statistical learning on both non-linguistic continuous sound streams and visual shape sequences. Evidence from these researches suggest that statistical learning is involved in discovering and extracting regularities, and it is domain-general. However, statistical learning in different domains is constrained by domain-related factors. For example, statistical learning in language(s) is constrained by language-specific factors; while non-linguistic statistical learning is constrained by stimulus characteristics and presentation modality. In recent years, several studies have examined the temporal course of statistical learning by employing event-related potentials (ERPs) technique and investigated its neural substrates by using functional magnetic resonance imaging (fMRI) technique. ERPs studies consistently found that a negative ERP component at around 400 ms was related with the extraction of regularities, and findings of fMRI studies suggested that statistical learning mainly involved left superior temporal gyrus, right striatum and right medial temporal memory system.