abstract: We investigate the effect of a spatio-temporal disorder onto diffusion-limited reactions and related first-passage phenomena in dynamic heterogeneous media such as polymer solutions or the cytoplasm of living cells. Rapid re-arrangements of a medium constantly change the effective diffusivity felt locally by a diffusing particle. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realisation of an individual reaction event triggered by a single molecule. This counter-intuitive finding highlights the crucial role of dynamic spatio-temporal heterogeneities of the cytoplasm onto biochemical processes in living cells. Some further extensions and related open mathematical problems are discussed.