This talk presents the culmination of my PhD research on aspects of quantum and statistical field theories constrained to spatial subregions. The study delves into the information theoretic properties of statistical field theories, particularly focusing on the mutual information between disjoint spatial subregions. The findings on mutual information have implications for existing analogue QFT simulator experiments, since the infinite temperature limit of a QFT corresponds to a classical statistical field theory. Furthermore, an outlook is presented on possible future works, where our results on mutual information can be used to explore the quantum regime, aiming for a comprehensive description of mutual information in such simulators. Additionally, the time evolution of a quantum field restricted to a spatial subregion is investigated. Given the infinitesimal nearest-neighbour couplings in the action, this restriction leads to a non-unitary time evolution, characterising the system as open. This approach could provide new insights into local thermalisation and the emergence of effective hydrodynamic descriptions of quantum field dynamics, as used, for example, in the description of heavy ion collisions.