  Since the inception of the atomic force microscope AFM, dynamic methods have
been very fruitful by establishing methods to quantify dissipative and
conservative forces in the nanoscale and by providing a means to apply gentle
forces to the samples with high resolution. Here we review developments that
cover over a decade of our work on energy dissipation, phase contrast and the
extraction of relevant material properties from observables. We describe the
attempts to recover material properties via one dimensional amplitude and phase
curves from force models and explore the evolution of these methods in terms of
force reconstruction, fits of experimental measurements, and the more recent
advances in multifrequency AFM.
