The results of recent works dealing with uniform quasi-classical description of the basic quantities appearing in the theory of atomic scattering (S-matrix, amplitude, and differential and total scattering cross sections) are reviewed. The above-listed quantities are expressed in the form of multiple integrals calculated by the saddle-point method. The cases with two and three saddle points and also a specific case arising in calculation of total cross sections are analyzed. An analytical extrapolation of the formula for a differential cross section to the region of classically forbidden trajectories and a uniform formula for the total cross section of inelastic transition are suggested for the first time. The formulas can also be used to describe photon and electron spectra produced by atomic collisions.