The classical and lectin pathways of complement are major recognition systems of innate immunity that are found in mammals and other animal species. By means of several multimolecular proteases – C1, the mannan-binding lectin (MBL)–MBL-associated serine protease 2 (MBL–MASP-2) and the ficolin–MASP-2 complexes – each comprising a recognition protein and a protease component, they detect pathogens and other targets and thereby trigger proteolytic reactions. Both pathways converge to the formation of C3 convertase, a complex protease that cleaves C3, the central component of the complement system. Proteolytic cleavage of C3 generates a series of fragments and elicits various effector mechanisms, including inflammation and phagocytosis. These mechanisms contribute to the elimination of pathogenic microorganisms and altered host cells from blood and tissues and modulate the adaptive immune response. Key Concepts: C1q, MBL and ficolins are pattern-recognition molecules able to sense conserved motifs on pathogens and altered self-cells. C1q is a major sensor of apoptotic cells and regulator of immune tolerance. Proteolytic cleavage of C3 is pivotal for amplification of the complement response and labelling of the target particles. Target recognition, proteolysis and complex formation generate conformational changes that underlie complement functioning. Complement activation and activity are tightly regulated to avoid noxious side effects on normal host cells and tissues. Keywords: altered self-cells clearance; innate immunity; inflammation; pathogens; pattern recognition; phagocytosis; proteolysis