Interpreting quantum mechanics (QM) is taken as the interpretation of a practice involving both experimental and theoretical inferences. The two inference systems rest on mutually incompatible foundations. Thus, the theory disallows sharp particle trajectories. The accelerators and detectors basic to the practice of particle physics rely on sharp trajectories. Orthodox QM includes a projection postulate, allowing for the infusion of experimental inferences into the theory. A replacement for orthodox QM should include an analog of the projection postulate. It should also have a quantum, rather than a semi-classical, foundation and should accommodate virtual processes. The Consistent Histories (CH) formulation/interpretation meets these requirements. Here this is presented in two stages. The first summarizes Griffiths's formulation of CH and considers the outstanding objections The second treats the Gell-Mann–Hartle project of providing a CH formulation that allows for the emergence of a quasi-classical order, an approximation to the large-scale deterministic laws that characterize the classical realm.