In this talk we report our ongoing work about UQ of multi-physics and multi-domain coupled problems. In the multi-physics we consider the transport of pollutants from an urban drainage system to a groundwater reservoir due to a leaky pipe, with the final goal of doing a forward UQ analysis of the concentration of the pollutant at a probe point, e.g., a water well for agricultural purposes. In the multi-domain problem we consider the dynamics of populations of molecules and cells in a so-called organ-on-chip device; the geometry of these devices is complex and consisting of several smaller components, such that it is natural to solve the equations with a multi-domain approach. In this case, the final goal is a forward UQ analysis of biologically relevant quantities, such as the total amount of cells in the device at a certain time. In both cases, we would like to employ surrogate-models to perform the UQ analysis, and to build these surrogates with a collocation approach (single-fidelity or possibly multi-fidelity). The underlying mathematical question is thus whether computing surrogate models for each component separately and then combining them for the UQ analysis is more convenient than a monolithic/black box approach in which a single surrogate for the coupled model is employed. One technical issue with the decoupled approach is that connecting surrogate models may require encoder-decoder-like mechanisms to reduce the amount of information to be passed between surrogates.