Kraft pulping of wood is based on efficient depolymerization and solubilization of lignin, while cellulose is relatively undamaged. Non-cellulose cell wall polysaccharides are however in some cases heavily degraded, especially pectin and to a lesser degree also glucomannan while, xylan is relatively stable. In this mini-review, the most important reactions in lignin and polysaccharide degradation in kraft pulping are described, both the technically favorable and the problematic reactions, and the chemical background to discuss the advantages and drawbacks of the process. An attempt to put the different reactions in the perspective of the goals of the pulping process is made and a special focus is on the development of color in the pulp fiber during the kraft pulping.