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In Einstein's theory of general relativity, the causal structure of spacetime is itself dynamical. Causality is encoded into the geometry of light cones that bend under the influence of gravity. Quantum theory, on the other hand, tells us that nature is intrinsically probabilistic. A sharply defined causal structure, as it appears in classical general relativity, contradicts quantum theory. A more general framework is needed. In this talk, I present a research programme in quantum gravity to develop a mathematical understanding of the causal structure at the quantum level. This is, in fact, a problem common to different approaches to quantum gravity, from holography, to the perturbative S-matrix approach and loop quantum gravity. After a brief introduction into the conceptual aspects of the problem, I will report on several new results on this frontier. First, I explain how to construct physical observables using the light cone geometry. Then, building upon earlier results in loop quantum gravity, we take the description to the quantum level. Finally, I explain how a fundamental quantum discreteness of geometry can alter the spectrum of highly luminous gravitational wave events. The talk is based on arXiv:2504.10802,2402.12578, 2401.17491, 2104.05803.