An increasingly important part of chemistry, solid-state physics, and materials science takes place at the computer, allowing for new understanding, a reduction of experimental trial-and-error procedures, and energy and money savings. This requires highly accurate reproduction of phenomena at different scales, but the quantum scale (electrons) is by far the most challenging. Because it is an excellent compromise between accuracy and computational cost, Density Functional Theory (DFT) is the method of choice for the electronic structure problem. Although exact in principle, in practical applications DFT must rely on approximations, which may fail sometimes in unexpected ways, hampering the overall predictive power of computational chemistry, solid-state physics and materials sciences. The two main challenges for current DFT methodologies are strong correlation and long-range dispersion (van der Waals) interactions. Strong correlation occurs in systems in which the interaction between the electrons disrupts the physics of the underlying non-interacting model system of DFT. Long-range dispersion interactions are inherently non local and arise from the electrodynamic coupling between charge fluctuations in matter. They are omnipresent in chemistry, biology, and physics, determining protein folding, the structure of DNA, the physics of layered materials, just to name a few examples. These two fundamental problems have been usually kept separated in the literature, with very different - often empirical and ad hoc- strategies proposed to deal with them. The main goal of my Vici project is to develop a theoretical methodology in a pure DFT formalism to treat dispersion interactions, in a unified framework with strong correlation, using in a new way results in the limit in which the interactions between the electrons become infinitely strong.