Microtubules are essential cellular polymers assembled from tubulin heterodimers. The tubulin dimer consists of a compact folded globular core and intrinsically disordered C-terminal tails. The tubulin tails form a lawn of densely grafted, negatively charged, flexible peptides on the exterior of the microtubule, potentially akin to brush polymers in the field of synthetic materials. These tails are hotspots for conserved, chemically complex posttranslational modifications that have the potential to act in a combinatorial fashion to regulate microtubule polymer dynamics and interactions with microtubule effectors, giving rise to a "tubulin code". In this review, I summarize our current knowledge of the enzymes that generate the astonishing tubulin chemical diversity observed in cells and describe recent advances in deciphering the roles of tubulin C-terminal tails and their posttranslational modifications in regulating the activity of molecular motors and microtubule associated proteins. Lastly, I outline the promises, challenges and potential pitfalls of deciphering the tubulin code.