Ultracold atoms and their non-equilibrium evolution present an ideal platform to study fundamental processes of quantum field theory and the relaxation dynamics of quantum many-body systems. Here, we present recent results and future prospects for analogue quantum simulators based on effective field theory descriptions. In particular, we discuss the relaxation in an inhomogeneous extended bosonic Josephson junction and its connection to the sine-Gordon model, superradiant instabilities and recurrences in multiquantum vortex decay, common sound-rings during the relaxation of vortex clusters, and measurement of the analogue circular Unruh effect via local interferometric two-frequency detectors. The continuous non-destructive measurements of cold atom systems paves the way to study this fundamental and yet still untested prediction of quantum field theory, that a linearly accelerated observer in the vacuum observes a thermal state at the Unruh-temperature.