The most common preparative method for inorganic solids is solid state reaction of constituent materials. Since the solid state reaction is usually performed at high temperature for a long heating duration, almost all the products are thermodynamically stable. During the long history of solid state chemistry and materials science, an enormous number of binary and ternary equilibrium phase diagrams were constructed and it seems like there is no hope to find out new materials those exhibit fascinating functionality. By applying external fields to solid state reaction systems, however, it has become possible to synthesize new compounds those do not exist in the equilibrium phase diagrams. In this article, synthesis of inorganic materials under high-pressure and microwave electromagnetic fields is reviewed. The scope of this review covers, but is not limited to, effects of external fields (high-pressure and microwave electromagnetic wave) on the formation of new compounds and structures those can not be prepared by conventional synthetic routes.