Over the last 15 years, researchers have applied theories of continuum contact mechanics to nanotribology measurements to determine fundamental parameters and processes at play in nanometer-scale contacts. In this paper we discuss work using the atomic force microscope to determine nanoscale adhesion and friction properties between solids. Our focus is on the role that continuum contact mechanics plays in analyzing these measurements. In particular, we show how the JKR-to-DMT transition is taken into account, as well as limitations involved in using these models of contact in the presence of adhesion.