Аннотация:This review presents the mechanisms of formation for the angular and energy distributions of atoms sputtered from solid surfaces under ion bombardment with a focus on the complex influence of surface structure and interatomic interactions. The history of the construction of Sigmund's theory and its limitations are briefly discussed. The main models of ion sputtering are examined, which are divided into two groups: cascade and surface models. Traditional cascade models, though effective for amorphous and polycrystalline targets, are shown to be insufficient for accurately describing ejection from single-crystal surfaces. The widely known Silsbee’s focuson theory, a type of cascade theory, provides an explanation for Wehner spots observed in the sputtering of single crystals; however, it encounters significant difficulties at low incident ion energies. On the contrary, surface sputtering models are more successful in describing the features of angular and energy distributions of sputtered atoms, as they take into account the processes occurring with the emitted atoms after they exit the collision cascade. During the above-surface scattering of emitted atoms, a strong redistribution of angles and energy occurs due to the blocking effect, which cannot be described solely by a planar potential barrier. Additionally, analytical models of a discrete surface are discussed, in which the emitted atom is scattered by a single surface atom or by a lens formed by two surface atoms. It is concluded that more sophisticated models have to be taken into account to predict sputtering behavior more precisely, contributing to improved theoretical frameworks for surface dynamics and material analysis under ion irradiation.