motivated by the study of greedy algorithms for graph coloring, we introduce a new graph parameter, which we call weak degeneracy. this notion formalizes a particularly simple way of ``saving" colors while coloring a graph greedily. it turns out that many upper bounds on chromatic numbers follow from corresponding bounds on weak degeneracy. in this talk i will survey some of these bounds as well as state a number of open problems. this is joint work with eugene lee.