Models of chemical bonding are essential for contemporary chemistry. Even the explosive development of the computational resources including, both hardware and software, cannot eliminate necessity of compact, intuitive, and efficient methods of representing chemically relevant information. The Lewis model of chemical bonding, which was proposed eleven years before the formulation of quantum theory and preserves its pivotal role in chemical education and research for more than ninety years, is a vivid example of such a tool. As chemistry shifts to the nanoscale, it is becoming obvious that a certain shift of the paradigms of chemical bonding is inescapable. For example, none of the currently available models of chemical bonding can correctly predict structures and properties of sub-nano and nanoclusters. Clusters of main-group elements and transition metals are of major interest for nanotechnology with potential applications including catalysis, hydrogen storage, molecular conductors, drug development, nanodevices, etc. Thus, the goals of this dissertation were three-fold. Firstly, the dissertation introduces a novel approach to the description of chemical bonding and the algorithm of the software performing analysis of chemical bonding, which is called Adaptive Natural Density Partitioning. Secondly, the dissertation presents a series of studies of main-group element and transition-metal clusters in molecular beams, including obtaining their photoelectron spectra, establishing their structures, analyzing chemical bonding, and developing generalized model of chemical bonding. Thirdly, the dissertation clarifies and develops certain methodological aspects of the quantum chemical computations dealing with clusters. This includes appraisal of the performance of several computational methods based on the Density Functional Theory and the development of global optimization software based on the Particle Swarm Optimization algorithm.