Operator preconditioning offers a general recipe for constructing preconditioners for discrete linear operators that have arisen from a Galerkin approach. The key idea is to employ matching Galerkin discretizations of operators of complementary mapping properties. If these can be found, the resulting preconditioners will be robust with respect to the choice of the bases for trial and test spaces. In particular, in a finite element setting, they will still perform well even for high-resolution models. Operator preconditioning has a wide range of applications in various areas. It is a generic approach for building preconditioners for variational saddle-point problems and it offers a canonical way to deal with complex-valued problems. Under the name of dual-mesh Caler´on preconditioning, the it has also become a powerful technique to accelerate iterative solvers for boundary element methods for first-kind boundary integral equations in computational acoustics and electromagnetics.