The quantum and semi-quantum mechanics of rigid molecules rotating in static electric and intense nonresonant laser fields have been studied. Basic quantum features including energy level correlation diagrams, eigenfunctions, alignment, orientation, and time-dependent wave functions propagated under pulsed fields are calculated. Energy level nearest neighbor spacing disributions are the primary semi-quantum approach, but Husimi distributions, periodic orbits, and monodromy diagrams are also investigated. We have elucidated these facets of the quantum-classical correspondence in this important rotational model, which is classically nonscaling with mixed phase space.