The quantum theory of measurement has led to tremendous improvements in metrology that offer a quantum advantage over classical measurement protocols while at the same time shedding light on the foundations of quantum theory itself. In this seminar, I will review the modern description of a quantum measurement in three levels of detail: as a positive operator-valued measure, as a completely positive trace-preserving map, and as a system-apparatus interaction. These descriptions of a quantum measurement will then be applied to three distinct gravitational scenarios. The first application will be in the context of QFT on curved spacetime, where I will introduce an operational characterization of entanglement and show its sensitivity to spacetime structures such as global topology, black holes, and gravitational waves. The second application will be the construction of time observables and their use in relational quantum theories. The third application will place the ultimate bound on the precision to which we can hope to observe the nonlinear gravitational wave memory effect.