We start with a very short introduction to the field of descriptive combinatorics and offer, as motivation for its study, a connection to both classical descriptive theorems as well as basis results in graph theory. Concretely, we showcase the $G_0$ dichotomy as a graph version of an old theorem of Cantor and present some recent variations of this result, namely the $L_0$ dichotomy, the proof of which will take up most of the talk. If time permits, we briefly contrast the dichotomy results with some recent and well-known negative basis theorems.