Like all binary stars, binary systems of two white dwarfs (WDs) can be found in two states: detached and interacting. The difference between the two states is that interacting systems are close enough that matter is able to flow off the surface of one star (the donor) onto the other (the accretor). In detached systems this is not the case. WD-WD binaries begin their lives as detached systems and in some cases can evolve to become interacting (or "come into contact" as we say in the business). When this occurs, various outcomes may result----e.g., Type Ia supernova, merger events, or the more mundane continued evolution as an interacting binary. Various, and somewhat uncertain, physics determine which outcome occurs in which cases, making this early contact phase an interesting and rich area of study.
In this talk, I will discuss generally the physics that determines how a WD-WD binary system evolves, paying particular attention to the interplay between the donor's and orbit's evolution that determines the occurrence and rate of mass transfer. I will then discuss the AM CVn population. This class of binaries is an example of objects that survived the contact phase, giving us clues as to which systems do survive contact. I will discuss my own work on these systems and how we might read these clues. Finally, I'll return to the contact phase of potential AM CVn progenitors. As a means to highlight indicated future work, I'll discuss the physics of accretor spin-up as a destabilizing mechanism and the occurrence of He ignition events on the accretor's surface.