Dynamic Atomic Force Microscopy (AFM) modes, where the cantilever is vibrated while the sample surface or tip is scanned, belong to the standard features of most commercial instruments. With these techniques images can be obtained the contrast of which depend on the elasticity of the sample surface. Quantitative determination of Young's modulus of a sample surface with AFM is a challenge, especially when stiff materials such as hard metals or ceramics are encountered. The evaluation of the cantilever vibration spectra at ultrasonic frequencies provides a way to discern local elastic data quantitatively using the flexural vibration modes. Nanocrystalline magnetic materials, multi- domain piezoelectric materials, polymeric materials, diamond-like carbon layers, silicon, and soft clay have been examined. Images obtained at the contact resonance frequencies are presented whose contrast is based on the elastic differences of the surface structure of the various materials examined. The spatial resolution is approximately 10 nm. Applying an electrical ac-field between the tip and the surface of a piezoelectric sample, images can be generated whose contrast is additionally influenced by the piezoelectric and dielectric properties of the sample. Furthermore, we present a new approach for studying friction and the stick-slip phenomenon using the torsional resonances of AFM cantilevers.