Theoretical bioinorganic and biomimetic chemistry involves the careful description of the electronic structure: for example, 'valence bond reading' of broken-symmetry density functional theory computations gives insight into the structure and bonding of metal-radical systems with complex electronic structures. Exploring the reactivities of such systems leads to the design of novel compounds with better reactivities. Combined quantum-mechanics/molecular-mechanics (QM/MM), where the QM part is a sophisticated ab initio method, aids in understanding nature's most complicated reaction mechanisms in atomic detail. First principles molecular dynamics simulations (Car-Parrinello simulations) open up exciting new avenues for studying transition metal centers and enable several questions to be addressed that cannot be resolved with either standard quantum chemical or traditional force-field methods.