Seismic tomography shows that subducting slabs can either sink straight into the lower mantle, or lie down in the mantle transition zone. Moreover, some slabs seem to have changed mode from stagnation to penetration or vice versa. We investigate the dynamic controls on these modes and particularly the transition between them using 2D self-consistent thermo-mechanical subduction models. Our models confirm that the ability of the trench to move is key for slab flattening in the transition zone. Over a wide range of plausible Clapeyron slopes and viscosity jumps at the base of the transition zone, hot young slabs (25 Myr in our models) are most likely to penetrate, while cold old slabs (150 Myr) drive more trench motion and tend to stagnate. Several mechanisms are able to induce penetrating slabs to stagnate: ageing of the subducting plate, decreasing upper plate forcing, and increasing Clapeyron slope (e.g. due to the arrival of a more hydrated slab). Getting stagnating slabs to penetrate is more difficult. It can be accomplished by an instantaneous change in the forcing of the upper plate from free to motionless, or a sudden decrease in the Clapeyron slope. A rapid change in plate age at the trench from old to young cannot easily induce penetration. On Earth, ageing of the subducting plate (with accompanying upper plate rifting) may be the most common mechanism for causing slab stagnation, while strong changes in upper plate forcing appear required for triggering slab penetration.