Titanium dioxide (TiO2) is one of the most widely used nanomaterials in many emerging areas of material science, including solar energy harvesting and biomedical implanting. In this review, we present progress and recent achievements in the theory and computer simulations of the physicochemical properties of small TiO2 clusters, middle-size nanoparticles, as well as the liquid-solid interface. The historical overview and the development of empirical force fields for classical molecular dynamics (MD) of various TiO2 polymorphs, such as rutile, anatase, and brookite, are given. The adsorption behavior of solvent molecules, ions, small organic ligands, and biomacromolecules on TiO2 interfaces are examined with the aim of the understanding of driving forces and mechanisms, which govern binding and recognition between adsorbate and surfaces. The effects of crystal forms, crystallographic planes, surface defects, and solvent environments on the adsorption process are discussed. Structural details and dynamics of adsorption phenomena, occurring at liquid-solid interfaces, are overviewed starting from early empirical potential models up to recent reactive ReaxFF MD simulations, capable of capturing dissociative adsorption of water molecules. The performance of different theoretical methods, ranged from quantum mechanical (QM) calculations (ab initio and the density functional theory) up to classical force field and hybrid MM/QM simulations, is critically analyzed. In addition, the recent progress in computational chemistry of light-induced electronic processes, underlying the structure, dynamics, and functioning of molecular and hybrid materials is discussed with the focus on the solar energy applications in dye-sensitized solar cells (DSSC), which are currently under development. Besides, dye design principles, the role of anchoring moiety and dye aggregation in the DSSC performance are crucially analyzed. Finally, we outline the perspectives and challenges for further progress in research and promising directions in the development of accurate computational tools for modeling interactions between inorganic materials with not perfect structures and natural biomacromolecules at physiological conditions.