This review provides an overview of descriptions of atoms applied to the understanding of phenomena like chemical reactivity and selectivity, pKa values, Site of Metabolism prediction, or hydrogen bond strengths, but also the substitution of quantum mechanical calculations by machine learning models for energies, forces or even spectrosocopic properties and finally the fast calculation of atomic charges for force field parametrization. The descriptor space ranges from derivatives of the wavefunctions or electron density via quantum mechanics derived descriptors to classical descriptions of atoms and their embedding in a molecule. The common denominator for all approaches is the thorough understanding of the physics of the chemical problem that guided the design of the atom descriptor. Quantum mechanics (QM) and machine learning (ML) finally are converging to a new discipline, namely QM/ML.