Recent years have seen growing interest in the use of metrics inspired by complexity science for the study of consciousness. Work in this field has shown remarkable results in discerning conscious from unconscious states, and in characterizing states of altered conscious experience following psychedelic intake as involving enhanced complexity. Here, we study the relationship between complexity and a different kind of altered state of consciousness: meditation. We provide a scoping review of the growing literature studying the complexity of neural activity in meditation, disentangling different families of measures, short-term (state) from long-term (trait) effects, and meditation styles. Beyond families of measures used, our review uncovers a convergence toward identifying higher complexity during the meditative state when compared to waking rest or mind-wandering and decreased baseline complexity as a trait following regular meditation practice. In doing so, this review contributes to guide current debates and provides a framework for understanding the complexity of neural activity in meditation, while suggesting practical guidelines for future research.