A charted omega-category is like a strict omega-category, but instead of a globular set, it has an underlying regular polygraph: its cells have more complex pasting diagrams “charted” on their boundary. Several features of omega-categories generalise nicely, including joins and the monoidal biclosed structure of lax Gray products. I will detail some of the combinatorics involved, going deeper into the theory of globular posets than in my talk last July (which is not a prerequisite).