The review focusses on the fundamental importance of non-covalent interactions in nature by illustrating specific examples from chemistry, physics and the biosciences. Laser spectroscopic methods and both ab initio and molecular modelling procedures used for the study of non-covalent interactions in molecular clusters are briefly outlined. The role of structure and geometry, stabilization energy, potential and free energy surfaces for molecular clusters is extensively discussed in the light of the most advanced ab initio computational results for the CCSD(T) method, extrapolated to the CBS limit. The most important types of non-covalent complexes are classified and several small and medium size non-covalent systems, including H-bonded and improper H-bonded complexes, nucleic acid base pairs, and peptides and proteins are discussed with some detail. Finally, we evaluate the interpretation of experimental results in comparison with state of the art theoretical models: this is illustrated for phenol...Ar, the benzene dimer and nucleic acid base pairs. A review with 270 references.