The electronic structure at the interface between organic molecules and inorganic matter, metals in particular, plays a crucial role for numerous applications. In, e.g., organic and molecular electronics, the alignment of the molecular levels with the metal Fermi energy as well as the modification of the metal work function upon chemi- or physisorption of organic molecules are crucial parameters for device performance and functionality. Fundamental insight into the microscopic processes governing the interfacial electronic structure can be obtained from first-principles studies based on density-functional theory. First, some examples for its applicability to predict experimentally observable quantities are given and, subsequently, the interface between noble metal substrates and chemisorbed self-assembled monolayers of (dipolar) organic molecules is discussed. Analysis of interfacial charge transfer together with electrostatic considerations allows establishing a comprehensive picture for the adsorbate-induced work-function modification of metals, the mutual alignment of the energy levels at the metal/organic interface, and the relation between these two aspects. Finally, a brief account on the impact of out findings on ballistic electron transport through individual molecules will be given together with an outlook towards applications in molecular electronic devices.