The article reviews the present status of the theory of weak interactions of elementary particles at high energies and large momentum transfers; in the spatial picture this corresponds to short distances. The usual four-fermion V--A theory of weak interactions and the theory with intermediate $W$ boson are considered. Special attention is paid to virtual processes, particularly hadron-lepton and nonlepton weak interactions (weak neutral currents, $K_L^0$ and $K_S^0$ meson mass difference, hadronic processes with strangeness and parity change). It is shown that a theoretical investigation of these processes in the comparison of its results with experiment leads to serious contradictions in the theory. Different ways out of the difficulties existing in the theory are discussed.