In animal cells, centrosomes nucleate microtubules that form polarized arrays to organize the cytoplasm. Drosophila presents an interesting paradox however, as centrosome-deficient mutant animals develop into viable adults. To understand this discrepancy, we analyzed behaviors of centrosomes and microtubules in Drosophila cells, in culture and in vivo, using a combination of live-cell imaging, electron microscopy, and RNAi. The canonical model of the cycle of centrosome function in animal cells states that centrosomes act as microtubule-organizing centers throughout the cell cycle. Unexpectedly, we found that many Drosophila cell-types display an altered cycle, in which functional centrosomes are only present during cell division. On mitotic exit, centrosomes disassemble producing interphase cells containing centrioles that lack microtubule-nucleating activity. Furthermore, steady-state interphase microtubule levels are not changed by codepleting both γ-tubulins. However, γ-tubulin RNAi delays microtubule regrowth after depolymerization, suggesting that it may function partially redundantly with another pathway. Therefore, we examined additional microtubule nucleating factors and found that Mini-spindles, CLIP-190, EB1, or dynein RNAi also delayed microtubule regrowth; surprisingly, this was not further prolonged when we codepleted γ-tubulins. Taken together, these results modify our view of the cycle of centrosome function and reveal a multi-component acentrosomal microtubule assembly pathway to establish interphase microtubule arrays in Drosophila.