The polymer and plastic sectors are under the urge of mitigating their environmental impact. The need for novel and more benign catalysts for polyester synthesis or targeted functionalization led, in recent years, to an increasing interest towards cutinases due to their natural ability to hydrolyze ester bonds in cutin, a natural polymer. In this review, the most recent advances in the synthesis and hydrolysis of various classes of polyesters and polyamides are discussed with a critical focus on the actual perspectives of applying enzymatic technologies for practical industrial purposes. More specifically, cutinase enzymes are compared to lipases and, in particular, to lipase B from Candida antarctica, the biocatalyst most widely employed in polymer chemistry so far. Computational and bioinformatics studies suggest that the natural role of cutinases in attacking natural polymers confer some essential features for processing also synthetic polyesters and polyamides.