The nonlinear and stochastic dynamics of oscillating microcantilevers in the Atomic Force Microscope (AFM) are closely linked to the microscope's stability, resolution, minimum force detection, and the ability to generate material contrast. The bifurcations, stability, higher harmonics, and chaotic dynamics mechanisms are now well understood for vacuum and in air environments. This understanding has led to new imaging modes and stable operating conditions for the microscope. However there is a relative lack of understanding the nonlinear dynamics at play as the microscope is used in different ambient conditions such as in liquids on liquid-solid interfaces or when tapping on viscoelastic polymers in air or when exposed to multi-frequency excitation. In this talk we will discuss recent results that highlight some key challenges and opportunities in this area.