Responsive metal-organic frameworks (MOFs) that display sigmoidal isotherms triggered by discrete gas pressure-induced structural transformations are highly promising materials for energy related applications. However, their lack of transportability via continuous flow hinders their application in systems and designs that rely on liquid agents. We herein present examples of responsive liquid systems which exhibit a breathing behaviour and show step-shaped gas sorption isotherms, akin to the distinct oxygen saturation curve of haemoglobin in blood. Dispersions of flexible MOF nanocrystals in a size-excluded silicone oil form stable porous liquids exhibiting gated uptake for CO2, propane and propylene, as characterized by sigmoidal gas sorption isotherms with distinct transition steps. In situ X-ray diffraction studies show that the sigmoidal gas sorption curve is caused by a narrow pore to large pore phase transformation to the flexible MOF nanocrystals, which respond to gas pressure despite being dispersed in silicone oil. Given the established flexible nature and tunability of a range of MOFs, these results herald the advent of breathing porous liquids whose sorption properties can be tuned rationally for a variety of technological applications.