Field confinement at the junction between a biased scanning probe microscope's tip and solid surface enables local probing of various bias-induced transformations, such as polarization switching, ionic motion, and electrochemical reactions. The nanoscale size of the biased region, smaller or comparable to that of features such as grain boundaries and dislocations, potentially allows for the study of kinetics and thermodynamics at the level of a single defect. In contrast to classical statistically averaged approaches, this approach allows one to link structure to functionality and deterministically decipher associated mesoscopic and atomistic mechanisms. Furthermore, responses measured as a function of frequency and bias can serve as a fingerprint of local material functionality, allowing for local recognition imaging of inorganic and biological systems. This article reviews current progress in multidimensional scanning probe microscopy techniques based on band excitation time and voltage spectroscopies, including discussions on data acquisition, dimensionality reduction, and visualization, along with future challenges and opportunities for the field.