In this talk, I will present a broad overview of our efforts to incorporate certain generic implications of curved spacetime on quantum measurements. This requires an inherently non-local description of spacetime, beyond the usual one given by Einstein. A deeper look reveals a subtle interplay between non-locality and quantum effects, which can leave relics even at observational scales. The concluding part of the talk will describe some such relics – the Cheshire grin of a fundamentally non-local quantum spacetime.