Centrioles are structures that assemble centrosomes. CPAP is critical for centrosome assembly, and its mutations are found in patients with diseases such as primary microcephaly. CPAP's centrosomal localization, its dynamics, and the consequences of its insufficiency in human cells are poorly understood. Here we use human cells genetically engineered for fast degradation of CPAP, in combination with superresolution microscopy, to address these uncertainties. We show that three independent centrosomal CPAP populations are dynamically regulated during the cell cycle. We confirm that CPAP is critical for assembly of human centrioles, but not for recruitment of pericentriolar material on already assembled centrioles. Further, we reveal that CPAP insufficiency leads to centrioles with incomplete microtubule triplets that can convert to centrosomes, duplicate, and form mitotic spindle poles, but fragment owing to loss of cohesion between microtubule blades. These findings further our basic understanding of the role of CPAP in centrosome biogenesis and help understand how CPAP aberrations can lead to human diseases.