C1 is the multimolecular protease that triggers activation of the classical pathway of complement, a major element of antimicrobial host defense also involved in immune tolerance and various pathologies. This 790,000 Da complex is formed from the association of a recognition protein, C1q, and a catalytic subunit, the Ca2+-dependent tetramer C1s-C1r-C1r-C1s comprising two copies of each of the modular proteases C1r and C1s. Early studies mainly based on biochemical analysis and electron microscopy of C1 and its isolated components have allowed for characterization of their domain structure and led to a low-resolution model of the C1 complex in which the elongated C1s-C1r-C1r-C1s tetramer folds into a more compact, "8-shaped" conformation upon interaction with C1q. A major strategy used over the past years has been to dissect the C1 proteins into modular segments to characterize their function and solve their structure by either X-ray crystallography or nuclear magnetic resonance spectroscopy (NMR). The purpose of this review is to focus on this information, with particular emphasis on the architecture of the C1 complex and the mechanisms underlying its activation and proteolytic activity.