Abstract: Scientists' ability to design, synthesize, and optimize the properties of materials has underpinned much of the development of modern technology. In recent years, interest has rapidly grown in utilizing materials with complex electronic and/or structural properties to create devices with enhanced capabilities. In this talk, I will provide a broad view of the challenges for accurate numerical simulation of these types of systems, especially when accounting for realistic material-specific details. First, I will discuss a study of electron relaxation dynamics in nanomaterials relevant to the design of low-energy light emitters. A new semi-empirical pseudopotential formalism is developed which enables the accurate description of interactions between excited electrons and optical phonons in nanosystems. This reveals an unexpected and dramatic difference in the upper bound for electronic relaxation timescales between two well-studied nanomaterials: CdSe and CdS. Second, I will focus on the electronic structure of a two-dimensional array of ultracold Rb atoms relevant to emerging quantum technologies. Making use of new simulation methods based on tensor networks, I will describe how strong electron-electron interactions in this synthetic quantum "material" shape the complex quantum phase diagram of its ground state. These simulations provide a reinterpretation of recent experimental measurements, and reveal previously unknown quantum phases of matter.