In recent years the Feynman formulation of quantum theory with the use of functional integrals became the basis of numerical methods, mainly in the theory of gauge fields. This approach is discussed in detail in the present study using examples of quantum mechanical problems. In the case of several degrees of freedom $D$ this approach is substantially simpler and more powerful than the traditional approaches based on the Schrodinger equation: an average computer can handle problems with $D\sim$ 10. Possible applications are briefly discussed.