Biodegradable plastics (BPs) have attracted much attention since more than a decade because they can easily be degraded by microorganisms in the environment. The development of aliphatic-aromatic co-polyesters has combined excellent mechanical properties with biodegradability and an ideal replacement for the conventional nondegradable thermoplastics. The microorganisms degrading these polyesters are widely distributed in various environments. Although various aliphatic, aromatic, and aliphatic-aromatic co-polyester-degrading microorganisms and their enzymes have been studied and characterized, there are still many groups of microorganisms and enzymes with varying properties awaiting various applications. In this review, we have reported some new microorganisms and their enzymes which could degrade various aliphatic, aromatic, as well as aliphatic-aromatic co-polyesters like poly(butylene succinate) (PBS), poly(butylene succinate)-co-(butylene adipate) (PBSA), poly(epsilon-caprolactone) (PCL), poly(ethylene succinate) (PES), poly(l-lactic acid) (PLA), poly(3-hydroxybutyrate) and poly(3-hydoxybutyrate-co-3-hydroxyvalterate) (PHB/PHBV), poly(ethylene terephthalate) (PET), poly(butylene terephthalate) (PBT), poly(butylene adipate-co-terephthalate (PBAT), poly(butylene succinate-co-terephthalate) (PBST), and poly(butylene succinate/terephthalate/isophthalate)-co-(lactate) (PBSTIL). The mechanism of degradation of aliphatic as well as aliphatic-aromatic co-polyesters has also been discussed. The degradation ability of microorganisms against various polyesters might be useful for the treatment and recycling of biodegradable wastes or bioremediation of the polyester-contaminated environments.