The Borel chromatic number of an analytic graph is the definable counterpart of its chromatic number: instead of considering general colorings of pairs, we look at colorings with Borel sections only. It turns out - from the work from Kechris, Solecki and Todorcevic - that there exists a least possible Borel chromatic number among all analytic graphs: the one of $G_0$. In this talk, we will see how to separate uncountable Borel chromatic numbers between themselves, and from other cardinal characteristics of the continuum. We will also address some ongoing work on the graph generated by the Turing reducibility relation, and metric graphs defined for families of countable distances converging to zero.