To point to a few specifics, there seems to be a few possible interpretations, though I imagine someone else here could tell you more about the current consensus:
"Once the Schrödinger equation was given a probabilistic interpretation, Ehrenfest showed that Newton's laws hold on average: the quantum statistical expectation value of the position and momentum obey Newton's laws."
"Because quantum mechanics only reproduces classical mechanics in a statistical interpretation, and because the statistical interpretation only gives the probabilities of different classical outcomes, Bohr has argued that classical physics does not emerge from quantum physics in the same way that classical mechanics emerges as an approximation of special relativity at small velocities. He argued that classical physics exists independently of quantum theory and cannot be derived from it. His position is that it is inappropriate to understand the experiences of observers using purely quantum mechanical notions such as wavefunctions because the different states of experience of an observer are defined classically, and do not have a quantum mechanical analog."