Graph coloring is an important branch in graph theory. It came from the famous Four-Color Problem and is of wide application in time tabling, sequencing, scheduling, coding, frequency channel assignment, and other practical problems. Since this area includes quite a number of subjects and there exist too many interesting problems, only several interested subjects are selected in this chapter. An introduction of concepts and symbols on graph coloring is given in Sect. 1. Section 2 is devoted to discussing the classical vertex-coloring problem, involving the general upper bound of the vertex chromatic number, several well-known conjectures, and the colorability and choosability of planar graphs and graphs embeddable in a surface. Section 3 investigates the acyclic vertex-coloring and acyclic edge-coloring of graphs as well as their various generalizations such as star coloring, linear coloring, and acyclic improper coloring. Section 4 focuses on some progress on vertex-distinguishing edge-weighting problems. Two types of edge-weighting, i.e., proper edge-weighting and improper edge-weighting, are mentioned. The L(p, q)-labelling problem of graphs will be finally investigated in Sect. 5, including L(2, 1)-labelling, coloring of the square of a graph, injective coloring, backbone coloring, and (d, 1)-total-labelling. In each section, a somewhat detailed survey on the recent advance of the related direction and some open problems are provided.