In many frictional contacts, wear occurs in connection with a (local or global) relative movement between the contacting surfaces. Wear causes the surfaces to change tribologically in a wide variety of ways—depending on the dominant wear mechanisms; however, as this aspect of the huge research field of “wear” largely takes place beyond a purely contact-mechanical framework, we will not go into it further in this book. On the other hand, the change in profile geometry caused by wear is a largely contact-mechanical problem: as a result of the contact interaction, material is removed from the contacting surfaces and possibly fully removed from the contact. This changes the shape of the surfaces in the vicinity of the contact, which in turn modifies the solution to the contact problem—especially for the stress distribution in the contact area; the contact problem becomes a (time-dependent) wear-contact problem. In this chapter, we deal with contact-mechanical aspects of wear due to global sliding and “fretting” in plane contact problems.