The ability to track the statistical structure of language and more broadly, of our environment, is a key feature of our cognitive system. This process, known as statistical learning, is thought to rely on associative mechanisms, and notably chunking. In this review, we summarize recent empirical work on three main phenomena that have been consistently reported in the literature about chunking mechanisms: predictability effects, repetition spacing effects, and chunk size limits. To illustrate the generality and robustness of these phenomena, we show that they have been observed for the processing of both linguistic and visuo-motor sequences, in human and non-human primate studies. We discuss how current chunk-based models of statistical learning can account for these effects and highlight some of their limitations. Finally, we argue that recent neurocomputational models based on associative and Hebbian learning may provide new theoretical approaches to describe and better understand the nature of chunking mechanisms.