The separation of related molecules with similar physical/chemical properties is of prime industrial importance and practically entails a substantial energy penalty, typically necessitating the operation of energy-demanding low temperature fractional distillation techniques. Certainly research efforts, in academia and industry alike, are ongoing with the main aim to develop advanced functional porous materials to be adopted as adsorbents for the effective and energy-efficient separation of various important commodities. Of special interest is the subclass of metal-organic frameworks (MOFs) with pore aperture sizes below 5-7 Å, namely ultra-microporous MOFs, which in contrast to conventional zeolites and activated carbons show great prospects for addressing key challenges in separations pertaining to energy and environmental sustainability, specifically materials for carbon capture and separation of olefin/paraffin, acetylene/ethylene, linear/branched alkanes, xenon/krypton, etc. In this tutorial review we discuss the latest developments in ultra-microporous MOF adsorbents and their use as separating agents via thermodynamics and/or kinetics and molecular sieving. Appreciably, we provide insights into the distinct microscopic mechanisms governing the resultant separation performances, and suggest a plausible correlation between the inherent structural features/topology of MOFs and the associated gas/vapour separation performance.