One of the most remarkable features of our quantum universe is the wide range of time, place, scale, and epoch on which the deterministic laws of classical physics apply to an excellent approximation. This talk reviews the origin of such a quasiclassical realm in a universe governed fundamentally by quantum mechanical laws characterized by indeterminacy and distributed probabilities. We stress the important roles in this origin played by classical spacetime, coarse-graining in terms of approximately conserved quantities, local equilibrium, and the initial quantum state of the universe. The discussion is carried out first in the decoherent (or consistent) histories formulation of the quantum mechanics of closed systems (most generally the universe) assuming spacetime geometry is fixed. This is an Everettian generalization of the usual Copenhagen text book quantum mechanics of measurement situations that assumes the quasiclassical realm. Conversely we isolate the assumptions and approximations necessary to derive Copenhagen quantum mechanics from the more general quantum mechanics of closed systems. We describe a further generalization of usual quantum theory that is necessary to deal with quantum spacetime and describe under what conditions it predicts our observed coarse-grained classical spacetime that is a prerequisite for a quasiclassical realm.