The nonlinear energy sink (NES) is defined as a single-degree-of-freedom structural element with relatively small mass and weak dissipation, attached to a primary structure via essentially nonlinear coupling. It is a passive energy dissipation device designed to rapidly absorb vibration energy (due to shock, blast, earthquakes, etc.) from a primary structure and locally dissipate it. The article contains a mini-review of the works on NESs. Design schemes for single-sided and double-sided vibro-impact NESs (SSVI and DSVI NESs) are proposed on the basis of conceptual and design NES schemes that exist in the world scientific literature. The motion equations and the impact rule are given. The quasistatic Hertz contact law is adopted as the impact rule. Various representations of the impulsive loading on the primary structure are discussed. These are excitations by initial velocities only, periodic excitation, a shock in the half-sine form, single-sided periodic impulses of a rectangular shape,wind, seismic and broadband excitation. The Tables of some numerical parameters that can be accepted for VI NES are given. Using the presented data, the authors intend to investigate both the efficiency of SSVI and DSVI NESs under different types of impulsive load, and their dynamical behavior with the changing in their parameters.