Descriptive combinatorics studies problems from classical combinatorics, but where we restrict ourselves to only considering definable objects and definable witnesses to their combinatorial properties. For example, given a Borel graph, when can we find a Borel coloring of it with a given number of colors? We will use games and Borel determinacy to characterize for each $d$, exactly what Borel chromatic numbers can be attained by $d$-regular acyclic Borel graphs. If time permits, we will also discuss other problems such as matchings and edge colorings.