The main goal of our research program was the development of new methods for molecular modeling. Molecular modeling is indispensable for theoretical studies in chemistry, molecular physics, structural biology, the development of new materials, etc. Computer modeling is widely used world-wide for better understanding material properties and correlating structure with macroproperties, especially biological. Computer modeling is used not only in science but also in industry, of which the pharmaceutical industry leads. To effectively use molecular modeling methods, their theoretical foundation must be understood, and the method must be properly chosen. For this, it is necessary to thoroughly understand the range and reliability of the methods, which is key to evaluating and interpreting the calculated results. Some phenomena in the field of molecular biology and multicomponent reactions are explainable with molecular modeling. Developing algorithms for computer-based modeling of molecular structure and dynamics enables more accurate calculations and thus more effectively uses computer time for studying interesting molecules and allows longer simulations of complex systems. We have developed an explicit, symplectic method for simulating molecular dynamics (SISM), which is based on splitting the Hamiltonian of the system, allows the integration of the equations of motions using a long time step, is stable, is computationally economical, and can be effectively parallelized on distributed systems. We have demonstrated the effectiveness of the newly developed SISM method on a system of planar water molecules. The results of the simulation demonstrate that the SISM allows up to a six times longer time step than other, standard methods, while the structural and dynamical system properties agree very well with Leapfrog-Verlet method. The SISM calculates IR spectra (e.g., water) better than any other known method. In the field of developing methods for calculating the electronic structure of molecules using Green's functions, we have implemented numerous optimizations that lead to systematically improving the accuracy and speed of calculations. We have generalized the method to allow larger molecular systems to be considered. In studying water at the surface of proteins by using molecular dynamics simulations of a hydrated lysozyme, we have determined the chief mechanism for water density changes. The results indicate that the water density is closely correlated to the orientation of neighboring water molecules and thus their dipole interaction, in addition to the water molecules being affected by the local electrostatic field of the protein. In the field of developing QM/MM methods, we have developed the REPLICA/PATH method, which has been added to CHARMM, one of the most used programs for molecular dynamics simulations. We have extended the hybrid QM/MM method for calculating potential so that it is suitable for automatically determining transition states in chemical reactions. We have tested the method on some enzyme reactions. The results show close agreement of calculated transition state energies with the measured values. In the calculation of the simultaneous alpha addition of an cation and anion to an isocyanide, we have shown that the cations, anions, and isocynide directly form the alpha-adduct. An interesting question (especially in the field of combinatorial chemistry and drug design) arises from this result: is it generally true that ionic reactions of isocyanides progress as multicomponent reactions. No such studies have been performed theoretically and appropriate experiments can not be performed.