The open graph dichotomy states that the complete graph on the Cantor space is least among open graphs on analytic sets with respect to the ordering given by continuous graph homomorphisms. Ben Miller used dichotomies of this form to prove many interesting theorems in descriptive set theory.
I will survey some applications to the descriptive set theory of generalised Cantor spaces. I will further draw a connection to the Wadge hierarchy of generalised Cantor spaces and sketch what is currently known about its structure.