The study of impact oscillators is based on bifurcation theory as a condition monitor. Impact motion is characterised by parameters such as driving frequency and clearance. The possible bifurcations (period-doubling, saddle node and grazing) are investigated. Different types of impact chattering (complete, incomplete, periodic, chaotic and intermittent chattering) are found in different driving frequency regions. These dynamics are interpreted using impact maps and Poincaré maps, and impact resonance is predicted using analytic and numerical methods. Schemes for suppression of impact resonance are introduced using isolation subsystems. The characteristics of impact phenomena and the suppression schemes presented in this thesis are validated experimentally using a cantilever beam with an inelastic endstop.