The open graph dichotomy for a subset X of the Baire space states that any open graph on X either contains a large complete subgraph or admits a countable colouring. It is a definable version of the open colouring axiom for X and generalises the perfect set property. Recently, this was generalised to infinite dimensions by Miller, Carroy and Soukup. I will discuss extensions of this result to generalised Baire spaces and a number of applications such as variants of the Hurewicz dichotomy, the determinacy of Väänänen's game and the asymmetric Baire property. This is a joint project with Dorottya Sziraki.