This article is divided into two parts. In the first part, the atomic unit (au) system is introduced and the scales of time, space (length), and speed, as well as those of mass and energy, in the atomic world are discussed. In the second part, the utility of atomic units in quantum mechanical and spectroscopic calculations is illustrated with examples. It is shown that the system of atomic units can greatly facilitate calculations and unit conversions. In addition, a number of topics that can be fruitfully treated with the au system, including photoelectric effect, hydrogen atom and different Rydberg constants, positronium atom, atomic mass unit, nuclear binding energy, nuclear reaction energetics, annihilation and mass-energy interconversions, femtosecond and attosecond spectroscopies, quantum-size effects, excitons in semiconductors, and so forth are presented and discussed. (Contains 1 table and 1 figure.)