Cilia and flagella are surface-exposed, finger-like organelles whose core consists of a microtubule (MT)-based axoneme that grows from a modified centriole, the basal body. Cilia are found on the surface of many eukaryotic cells and play important roles in cell motility and in coordinating a variety of signaling pathways during growth, development, and tissue homeostasis. Defective cilia have been linked to a number of developmental disorders and diseases, collectively called ciliopathies. Cilia are dynamic organelles that assemble and disassemble in tight coordination with the cell cycle. In most cells, cilia are assembled during growth arrest in a multistep process involving interaction of vesicles with appendages present on the distal end of mature centrioles, and addition of tubulin and other building blocks to the distal tip of the basal body and growing axoneme; these building blocks are sorted through a region at the cilium base known as the ciliary necklace, and then transported via intraflagellar transport (IFT) along the axoneme toward the tip for assembly. After assembly, the cilium frequently continues to turn over and incorporate tubulin at its distal end in an IFT-dependent manner. Prior to cell division, the cilia are usually resorbed to liberate centrosomes for mitotic spindle pole formation. Here, we present an overview of the main cytoskeletal structures associated with cilia and centrioles with emphasis on the MTassociated appendages, fibers, and filaments at the cilium base and tip. The composition and possible functions of these structures are discussed in relation to cilia assembly, disassembly, and length regulation.