In this paper are put forward the basic principles under which all grinding machines, irrespective of size or type, must be constructed. The chief problems facing the designer of precision grinding machines are discussed, together with the essential elements and physical components. The choice of solutions which seem to offer the most promising future developments is suggested. The factors affecting the design of grinding machines—cost, ease of maintenance, and the influence of the user—and the essential elements—rigidity, accuracy, and constancy, are discussed. Mechanical and hydraulic traverse mechanisms are compared and a brief description is given of a typical hydraulic system. Although mechanical methods of traverse have been giving way to hydraulic systems, the author considers that with the improved electrical control gear available there may be a reversion to mechanical traverse mechanisms on account of their simplicity and reliability. The influences of the wheel-head and wheel-head spindles are discussed. The two lines of approach that wheel-head design and wheel-head speeds will follow during the next few years is suggested. Work-head and work-head drive arrangements are described; followed by the main features of universal machines and machines arranged for automatic operation. Finally, methods and mechanisms are described for obtaining concave and convex camber with roll-grinding machines.