This review presents the current advances in the theory of collision of slow electrons with molecules. First the fundamental experimental results are reviewed. Then main attention is paid to the semiphenomenological and modeling approaches to the problem. The adiabatic approximation and its application to calculating elastic scattering cross-sections and cross-sections for rotational transitions are treated. The long-wavelength approximation (effective-range theory) is presented in greater detail. The problem is discussed of taking account of rotation in the collision process. In particular, a mechanism is revealed of formation of dipole resonances in the scattering of an electron by a rotating polar molecule. Different semiphenomenological methods are treated for calculating the resonance vibrational excitation of simple molecules. The quasiclassical representation for the cross-sections for vibrational transitions in the theory of Herzenberg is discussed. This representation is applied to analyze the process of dissociative recombination. The model is treated of emergence of a term into the continuous spectrum and it is applied to explain the threshold resonances in the vibrational excitation cross-sections of certain molecules. The role is discussed of dipole interaction in forming these resonances. The results of the theoretical calculations are compared with the experimental data.