Scanning probe microscopies, especially scanning tunneling microscopy, were first directed to metal and semiconductor surfaces. Early challenges associated with the low conductivity and ionicity of oxides slowed application to even semiconducting ceramics. Recently, some of these obstacles have been overcome, and probe microscopies have been used to determine the atomic structures, as well as local properties, of many oxide surfaces and interfaces. Approaches to quantifying both tunneling spectroscopy and tunneling images of oxides are presented. Oxide surfaces accommodate nonstoichiometry via reconstruction or surface stabilization of substoichiometric phases. Effects of self-segregation and of impurity segregation on local properties of surfaces are observed directly. Three examples of local properties at interfaces are presented: contact potential at nanoscale metal cluster-oxide interfaces, local electrostatic fields at grain boundaries, and current flow in complex superconducting microstructures.