The advance of human civilization with materials development from the Stone Age to the Information Age is the starting point of Chapter 1, highlighting significant roles of computational design of materials. Important terms (model, simulation, database, and materials design) used in computational materials science are defined. The past and present development of computational design of materials is then introduced. A few milestones for alloy design, such as the Hume–Rothery rule, the Phase Computation (PHACOMP) method, and the calculation of phase diagrams (CALPHAD) approach, are highlighted. The past two-decade focus on three aspects in computational design of materials (multiscale/multilevel modeling methodologies, simulation software, and scientific database) in the core of the Materials Genome Initiative is emphasized. A general framework of materials design is demonstrated with two flowcharts: through-process simulation of Al alloys during heat treatment, and the three stages for the development of engineering materials. The two-part structure of the book – fundamentals and case studies – is explained.