The current paper presents a state-of-the-art review in the field of interaction of atomic and molecular clusters with solids. We do not attempt to overview the entire broad field, but rather concentrate on the impact phenomena: how the physics of the cluster-surface interaction depends on the kinetic energy and what effects are induced under different energetic regimes. The review starts with an introduction to the field and a short history of cluster beam development. Then fundamental physical aspects of cluster formation and the most common methods for the production of cluster beams are overviewed. For cluster-surface interactions, one of the important scenarios is the low-energy regime where the kinetic energy per atom of the accelerated cluster stays well below the binding (cohesive) energy of the cluster constituents. This case is often called This is the peer-reviewed author's version of a work that was accepted for publication in Surface Science Reports. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version