Since its introduction in 1986, atomic force microscopy (AFM) has been studied in depth to extend its capability as an advanced metrological tool at the atomic scale. One notable milestone in the advance of AFM was the development of dynamic mode operation. Since dAFM measurement is accomplished in a non-destructive manner with minimal stiction and high sensitivity, it is the most widely utilized operating mode across diverse applications. Even though most AFM users interpret the scanning results based on the linear theory by considering the shift of resonance with respect to the tip-sample interaction, the actual cantilever dynamics are far more complicated as the tip-sample interactions are highly nonlinear. One example is the occurrence of bi-stability in the dynamic response of the cantilever due to the highly nonlinear attractive and repulsive tip-sample interactions, which is manifested by the presence of chaotic oscillations and imaging artifacts in the acquired AFM images. We will address the complex nonlinear behavior of a AFM cantilever during tapping mode operations. Based on the better understanding about the cantilever dynamics, the strategies to find right settings and interpret the AFM results will be discussed. Another mode utilized to characterize a multi-functional material property on top of the morphological information is the contact resonance mode. For example, Piezoresponse Force Microscopy (PFM) applies an electrical voltage to a piezoelectric sample through a metal-coated AFM cantilever, in contact with the sample, to characterize the piezoelectric property. In PFM, the frequency of the voltage is often set to the contact resonance frequency of the cantilever to amplify the signal. One of the main issues is that the frequency is not constant, but variable with respect to the stiffness and morphology of the sample to produce artifacts. In order to address this issue, various strategies such as the dual AC resonance tracking (DART) and band excitation (BE) mode have been developed, which will be discussed in this workshop. Moreover, a new AFM cantilever design which can eventually stabilize the contact resonance frequency will be also introduced.