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I review the arguments most often raised against a fundamental coupling ofclassical spacetime to quantum matter. I show that an experiment by Page andGeilker does not exclude such a semiclassical theory but mandates an inclusionof an objective mechanism for wave function collapse. In this regard, I presenta classification of semiclassical models defined by the way in which the wavefunction collapse is introduced. Two related types of paradoxes that have beendiscussed in the context of the necessity to quantize the gravitational fieldcan be shown to not constrain the possibility of a semiclassical coupling. Athird paradox, the possibility to signal faster than light via semiclassicalgravity, is demonstrably avoided if certain conditions are met by theassociated wave function collapse mechanism. In conclusion, all currentlydiscussed models of semiclassical gravity can be made consistent withobservation. Their internal theoretical consistency remains an open question.

Three little paradoxes: making sense of semiclassical gravity