We present the foundations of quantum mechanics required to describe atoms and molecules. Starting from classical mechanics, Schrödinger’s equation is introduced, while many-particle systems are approached using the Hartree and Hartree-Fock methods. Different chemical bond types are discussed in this context, namely: ionic, covalent, hydrogen, and van der Waals bonds. Classical molecular dynamics calculations are shown to be employed in the investigation of systems with up to millions of atoms, but quantum-level calculations are essential for an accurate description of chemical bond breaking and formation in biomolecular systems. The essentials of density functional theory (DFT), detailing the Hohenberg-Kohn theorems and the Kohn-Sham strategy, are presented. Distinct exchange-correlation functional approximations are shown with their limitations and advantages, including hybrid functionals. Finally, the description of a fragmentation strategy to apply quantum methods in the study of protein–ligand interactions is discussed.