Interactions among tectonics, volcanism, and surface weathering are critical to the long-term climatic state of a terrestrial planet. Volcanism cycles greenhouse gasses into the atmosphere. Tectonics creates weatherable topography, and weathering reactions draw greenhouse gasses out of the atmosphere. Weathering depends on physical processes governed partly by surface temperature, which allows for the potential that climate-tectonic coupling can buffer the surface conditions of a planet in a manner that allows liquid water to exist over extended timescales (a condition that allows a planet to be habitable by life as we know it). We discuss modeling efforts to explore the level to which climate-tectonic coupling can or cannot regulate the surface temperature of a planet over geologic time. Thematically, we focus on how coupled climate-tectonic systems respond to the following: (1) changes in the mean pace of tectonics and associated variations in mantle melting and volcanism, (2) large-amplitude fluctuations about mean properties such as mantle temperature and surface plate velocities, and (3) changes in tectonic mode. We consider models that map the conditions under which plate tectonics can or cannot provide climate buffering as well as models that explore the potential that alternate tectonic modes can provide a level of climate buffering that allows liquid water to be present at a planet's surface over geological timescales. We also discuss the possibility that changes in the long-term climate state of a planet can feedback into the coupled system and initiate changes in tectonic mode.