One presents numerous approaches for the construction of variational principles for equations with operators which, in general, are nonpotential. One considers separately linear and nonlinear ordinary differential equations, partial and integropartial differential equations. One constructs and investigates both extremal and stationary variational principles and one gives applications of these principles in theoretical physics and in analytic mechanics. A series of unsolved problems are indicated. The survey is intended for mathematicians, physicists, working in both theoretical and applied areas, as well as for graduate students of physics and mathematics.