Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale. In this theory, spacetime takes the form of a random Lorentzian lattice known as a "causal set". In this talk, I will describe recent developments in defining interacting scalar quantum field theories on this novel background. I will present diagrammatic rules for computing in-in correlators; these rules are manifestly causal thanks to the appearance of the retarded propagator.
This framework is a step towards new quantum gravity phenomenology, since it enables the computation of early universe observables under the assumption that spacetime is fundamentally discrete.