Imbuing numerical algorithms with physical structure-preserving properties has led to a renaissance in physics-based simulations. These properties include, but are not limited to, conservation and dissipation of auxiliary quantities, preservation of key steady states or solution invariants. Mimicking such properties significantly improves the robustness and accuracy of simulations in a wide range of applications in science and engineering. This minisymposium focuses on the application of emerging structure-preserving techniques within complex fluids, including (but not limited to) multi-species and multi-phase flows, thermally perfect gases, and non-ideal equations of state.