What happens when the "hydrodynamic charges" are not conserved but either decay slowly or, if the system is open, are exchanged with the environment? This non-conservation violates one of the core principles of hydrodynamics meaning that, as it stands, hydrodynamics no longer applies to the situation. In these cases one must modify the hydrodynamic formalism to relaxed hydrodynamics/quasihydrodynamics, which is significantly less developed than hydrodynamics but incorporates "weak" non-conservation into the description. In this talk I will review recent developments including: how one can satisfy Onsager reciprocity relations, how to incorporate electrically driven ground states into the formalism, and how generalised relaxations can be built into the relaxation time approximation of kinetic theory. I will finish by describing, in my opinion, what big questions are still seeking answers.