Magnetic metal-organic complexes and coordination polymer frameworks can exhibit a transition between two different spin states of the integrated transition-metal ion, an attribute known as a spin-crossover (SCO) transition. This is a spectacular phenomenon that provides magnetic bi-stability and reversible spin-switchability to the material. Consequently, the magnetic state of the metal-organic center can be externally steered by temperature, pressure, or light irradiation. SCO molecules therefore are promising materials for various technological applications, such as spintronics devices, photo-switches, color displays, and information storage units. In spite of the importance of SCO materials in spintronics and other applications, the materials-specific understanding of the SCO phenomenon has remained a challenge. Here we survey recent developments in first-principles computational design of SCO metal-organic materials. A major outcome of recent state-of-the-art investigations is that an accurate quantitative description and even computational design of SCO materials can be provided by density functional theory-based electronic structure calculations combined with ab initio molecular dynamics simulations.