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The construction of thousands of well-defined, porous, metal–organic framework (MOF) structures, spanning a broad range of topologies and an even broader range of pore sizes and chemical functionalities, has fuelled the exploration of many applications. Accompanying this applied focus has been a recognition of the need to engender MOFs with mechanical, thermal and/or chemical stability. Chemical stability in acidic, basic and neutral aqueous solutions is important. Advances over recent years have made it possible to design MOFs that possess different combinations of mechanical, thermal and chemical stability. Here, we review these advances and the associated design principles and synthesis strategies. We focus on how these advances may render MOFs effective as heterogeneous catalysts, both in chemically harsh condensed phases and in thermally challenging conditions relevant to gas-phase …