I investigate materials properties of ferroelectric and ferromagnetic compounds with a variety of computational tools, namely density functional theory and phase-field modeling. By studying the atomistic picture, models can be parameterized to predict device-relevant behavior before any experiments are performed. This so-called hierarchical materials-by-design approach can uncover novel functionalities useful for applications. Within this research program, I also study multiferroics, ferroic compounds that display both magnetic and ferroelectric order. These materials are promising candidates for next-generation applications such as magnetoelectric logic memory or solar energy converters and my research efforts are focused on expanding the scientific understanding of their behavior at the nanoscale.