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The interest in cell aggregates is nowadays undergoing a strong acceleration because of the coincidence of technical advancements and experimental insights that excite theoretical challenges. In this respect, systems of great relevance are multicellular spheroids, where it is now possible to locally measure stress and fluid flow within the aggregate, thereby opening the path to quantitative theories to explain the role of mechanics in cell proliferation and motility. There is a well supported evidence that mechanical forces interfere with the development of solid tumors and arrest their proliferation. The coupling between cell mechanics, fluid flows, extra-cellular matrix and cell proliferation is however not trivial: malignant cells exhibit a complex rheology that accompanies an elusive mechanobiological feedback. Intriguingly, the role of fluid flows and stress is understood to be crucial in other cell aggregates, of completely different functionality: embryos exploit mechanics to generate shape and function, both in producing displacement such as lumen formation and in signaling cell-to-cell mutual positions and orientations.