Computational science draws upon applied mathematics, computer science, engineering, and the physical sciences. It is a multidisciplinary field that crosses the boundaries separating traditional fields of research from each other. Along with theory and physical experiment, it has become a third pillar of scientific investigation. In this talk, I motivate modern computational science by surveying the relationships between engineering, the physical sciences, computer science, and applied mathematics. I highlight several examples where the fusion of careful mathematics and computation were essential to tackle important real-world problems.