The possible ways and progress of infrared or red laser pumped green and blue laser emissions from a single solid state material doped by rare earth ions are outlined. The green and blue lasers realized from infrared laser pumped rare earth doped nonlinear laser crystals by means of self-frequency-conversion and from infrared laser pumped rare earth-doped bulk, fiber and microsphere materials by means of frequency upconversion are introduced in detail. Other kinds of devices and methods are also compared. The typical nonlinear laser crystals such as YAl3(BO3)4, GdAl3(BO3)4, YCa4O(BO3)3, GdCa4O(BO3)3, and the typical upconversion fluoride fibers are compared and analyzed. The major problems remaining to be solved and the developing trends in the area are also discussed.