AbstractNature’s enzymes are an ongoing source of inspiration for scientists. The complex processes behind their selectivity and efficiency is slowly being unraveled, and these findings have spawned many biomimetic catalysts. However, nearly all focus on the conversion of small molecular substrates. Nature itself is replete with inventive catalytic systems which modify, replicate, or decompose entire polymers, often in a processive fashion. Such processivity can, for example, enhance the rate of catalysis by clamping to the polymer substrate, which imparts a large effective molarity. Reviewed herein are the various strategies for processivity in nature’s arsenal and their properties. An overview of what has been achieved by chemists aiming to mimic one of nature’s greatest tricks is also included.