There are strong indications that in the 21st century, computational chemistry will be a prime research tool not only for basic science but it also will have a prominent position in life and material sciences. Recent developments in nanotechnology now allow us to detect a layer of single atoms. Researchers are able not only to image but also to manipulate molecules and atoms. In order to be able to make reliable predictions for systems with heavy elements, an efficient relativistic theory is needed. In chapter one, Y. Ishikawa and M.J. Vilkas provide a review of multireference Moller-Plesset (MR-MP) perturbation theory. Fifteen years ago Roberto Car of Princeton University and Michele Parrinello of Max Planck Institute introduced a method that revolutionized electronic structure calculations for molecules, liquids and solids. In addition, this method called the Car-Parrinello Method also opened die field of quantum molecular dynamics for physicists. Applications of the rigorous quantum mechanical (QM) calculations for large molecular systems, including clusters of the size that could allow for a proper representation of surfaces or solid states, are still beyond current computational techniques. The molecular mechanics (MM) methods, which can handle very large systems, do not account for quantum effects, which are essential for a majority of the studied problems. In the third chapter Isaac B. Bersuker describes the general theory of the QM/MM approach. A class of porous alumino-silicate materials called zeolites has been known for almost 300 years. They are best known for their role as catalysts. In chapter four, Marcel Allavena and David White present a review of applications of computational chemistry to the proton transfer, primary process for acid-base chemistry on zeolites. Theoretical studies on isolated clusters could be used to reveal their relationship to condensed phase analogues. Chapter five provides a review by S. Roszak and J. Leszczynski of recent data for the clusters formed from the charged ion and weakly interacting ligands. In such cases, the process of the cluster formation is mainly determined by the electric field generated by the central ion. The last chapter of the volume, contributed by Carlos R. Handy, is devoted to recent developments in the incorporation of Continuous Wavelet Transform analysis into quantum operator theory.