False vacuum decay plays a vital role in many models of the early Universe. However, we lack a satisfying theoretical understanding of this process, with existing approaches working only in imaginary (Euclidean) time, and relying on crucial assumptions that have yet to be empirically tested. An exciting route forward is to use cold-atom systems which undergo first-order phase transitions that are analogous to vacuum decay. In this talk, I will present recent theoretical work to understand this analogy using semiclassical lattice simulations, and will discuss possibilities and challenges for realising these analogues in the laboratory.