Plate tectonics and mantle convection are different aspects of the same, coupled system, yet mantle convection calculations do not exhibit plate tectonic behavior unless it is imposed by the modeler. This paper explores the quest for self-consistent incorporation of plate tectonics into mantle convection models, and presents new results and parameterizations. Simulations of convection with buoyant, deformable continents but no oceanic plates show that supercontinent cycling is a possible,

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... not required, aspect of the dynamics, and that the presence of even non-episodic continents has a profound effect on the spectrum of mantle heterogeneity. Ductile shear localization may be the key process for generating weak plate boundaries. Possible localization mechanisms can be described using time-dependent evolution equations, allowing evolving lithospheric strength heterogeneity with long-term memory. Steady-state versions of these rheologies are used to demonstrate the formation of weak transform boundaries in a 2-D model, and convergent, divergent and strike-slip boundaries in 3-D models. However, the present models are far from realistic; future directions and some philosophical issues are discussed.