Wear is the loss or displacement of material due to contact or relative motion between bodies. Wear plays an important role in the performance of tribological components and is undesirable in most machine applications. Wear is also important for small scale instruments such as the atomic force microscope (AFM). The AFM has become one of the most widely used tools in the fields of nanoscience and nanotechnology for the preparation and analysis of surfaces and materials. It has been shown that AFM tip wear affects the performance and operating life of the AFM used for applications such as nanomanufacturing, nanoscale metrology and probe-based data storage applications. As AFM techniques advance from use in research laboratories to industrial applications, the durability and stability of the tip itself become more critical. However, the fundamental wear mechanisms and how wear affects the performance of precision components at the nanoscale are not fully understood. Thus, it is necessary to explore the qualitative as well as quantitative nature of nanoscale wear. In this thesis, we studied the mechanisms of nanoscale wear in contact mode AFM and explored the effect of tip wear on topography measurement in amplitude modulation AFM using molecular dynamics (MD) simulation. We characterized wear in terms of the structural and chemical evolution of the sliding surfaces, which revealed that nanoscale wear can occur through both adhesion and abrasion. Wear during running-in was also studied and it was observed that crystalline materials may become amorphous before they are removed from the surface. We then studied the effects of load, adhesive strength and surface roughness on nanoscale wear, and the results suggested that it is possible to identify optimum sliding conditions to minimize wear. In addition, we developed a model of amplitude modulation AFM and studied the effect of nanoscale wear on topography measurement. It was found that the resolution of amplitude modulation AFM measurements could be correlated to tip size and this relationship was also affected by the deformation of the materials. This research provides important insights into the fundamental mechanisms of nanoscale wear, which will lead to a better understanding of this technologically important phenomenon that controls the failure of systems from the macroscale to the nanoscale, with substantial economic, energetic, and environmental impacts.