Impact interactions can excite complex nonlinear resonant responses in structures subjected to simple periodic excitation. The specific features of these resonances are concentration of high harmonics in corresponding waveforms, dependence of their behaviour on parameters and initial conditions, synergistic spatial effects, and generation of essential forces and stresses. An effective approach to analysis of these resonances was developed using special functions, called periodic Green functions. An introduction of these functions allows the regular study of resonant phenomena in vibro-impact systems based on structural presentations and without reference to differential equations of motion. The paper reviews some results on the application of periodic Green functions for analysis of resonant phenomena in vibro-impact structures with lumped and distributed parameters. The physical experiments support the results of analysis.