We review recent trends in the first-principles theoretical studies on catalysis. We first see the accuracy of first-principles calculations, especially, the accuracy of generalized gradient approximation (GGA). Then we see recent developments of ab initio thermodynamics and statistical mechanics to predict surface phase diagrams as functions of chemical potentials or pressures of gas phase molecules. We also review recent development of micro-kinetic modeling for complex catalytic reactions. Finally, we describe our recent studies on HCOOH decomposition on the TiO₂(110) surface and simulation of electrode surfaces.