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Mean field theories predict a transition to a regime of elastic behaviour when a supercooled liquid is cooled below the mode-coupling theory temperature T_MCT . According to Random First Order Transition theory, deep energy landscape minima are ubiquitous in this regime, but transitions between them are slow. As such, nucleation has been expected to play a key role in the sub-T_MCT dynamics of these systems, with structural evolution proceeding via the size-limited nucleation of droplets of "aperiodic crystal" within domains of different, incompatible states. In this talk, we present direct evidence from molecular dynamics simulations supporting the prediction of elasticity below T_MCT, but opposing that of nucleation. We find that dynamic facilitation, where local motion triggers further motion nearby, undergoes a crossover from short-ranged to elastic and long-ranged at T_MCT. However, upon studying the equilibration dynamics of initially out-of-equilibrium systems, we see no evidence of nucleation on the time sale of structural relaxation.