Since the inception of the atomic force microscope (AFM), dynamic methods (dynamic atomic force microscopy) 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 discuss 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. We further discuss open questions and key possible paths to advance the field.
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