This paper focuses on the development of constitutive models, commensurate system models, and inverse compensator construction for high speed nanopositioning in atomic force microscopes (AFM). All current AFM employ either stacked or cylindrical piezoceramic actuators for both longitudinal and transverse positioning of the sample. An inherent property of these materials is the presence of hysteresis and constitutive nonlinearities, even at the low drive levels employed for angstrom-level resolution. At low frequencies, standard feedback mechanisms effectively attenuate the hysteresis, whereas noise at high frequencies diminishes the efficacy of feedback and leads to unacceptable accuracy. In this paper, we discuss modeling techniques which provide a first step toward high speed nanopositioning for applications ranging from macroscopic product evaluation to real-time imaging of biological processes.