X-ray spectroscopy provides a number of experimental techniques that give an atom-specific projection of the electronic structure. When applied to surface adsorbates in combination with theoretical density functional spectrum simulations, it becomes an extremely powerful tool to analyze in detail the surface chemical bond. This is of great relevance to heterogeneous catalysis as discussed in depth for a number of example systems taken from the five categories of bonding types: (i) atomic radical, (ii) diatomics with unsaturated pi-systems (Blyholder model), (iii) unsaturated hydrocarbons (Dewar-Chatt-Duncanson model), (iv) lone-pair interactions, and (v) saturated hydrocarbons (physisorption).