Two major polymers of the cytoskeleton, actin filaments and microtubules, are assembled with expenditure of energy: the ATP/GTP tightly bound to actin/tubulin is irreversibly hydrolyzed to ADP/GTP during the assembly process, and liberation of Pi in the medium occurs subsequent to the incorporation of subunits in the polymer. Pi release acts as a switch, causing the destabilization of protein-protein interactions in the polymer, therefore regulating the dynamics of these fibres. An understanding of this regulation in vivo requires that progress be made in four areas: the chemistry of the NTPase reaction; the structure of the intermediates in nucleotide hydrolysis and the nature of the conformational switch; the regulation of parameters involved in dynamic instability of microtubules; and the possible involvement of nucleotide hydrolysis in the macroscopic organization of these polymers in highly concentrated solutions, compared with the simple case of a equilibrium polymers. Progress made along these lines will define trends for future investigation.