Ligands with a purely aliphatic backbone are receiving rising attention in the chemistry of coordination polymers and metal–organic frameworks. Such unique features inherent to the aliphatic bridges as increased conformational freedom, non-polarizable core, and low light absorption provide rare and valuable properties for their derived MOFs. Applications of such compounds in stimuli–responsive materials, gas, and vapor adsorbents with high and unusual selectivity, light-emitting, and optical materials have extensively emerged in recent years. These properties, as well as other specific features of aliphatic-based metal–organic frameworks are summarized and analyzed in this short critical review. Advanced characterization techniques, which have been applied in the reported works to obtain important data on the crystal and molecular structures, dynamics, and functionalities, are also reviewed within a general discussion. In total, 132 references are included.