Centrioles are microtubule-based cellular structures present in most human cells that build centrosomes and cilia. Proliferating cells have only two centrosomes and this number is stringently maintained through the temporally and spatially controlled processes of centriole assembly and segregation. The assembly of new centrioles begins in early S phase and ends in the third G1 phase from their initiation. This lengthy process of centriole assembly from their initiation to their maturation is characterized by numerous structural and still poorly understood biochemical changes, which occur in synchrony with the progression of cells through three consecutive cell cycles. As a result, proliferating cells contain three structurally, biochemically, and functionally distinct types of centrioles: procentrioles, daughter centrioles, and mother centrioles. This age difference is critical for proper centrosome and cilia function. Here we discuss the centriole assembly process as it occurs in somatic cycling human cells with a focus on the structural, biochemical, and functional characteristics of centrioles of different ages.