Synthetic biodegradable elastomers are a class of polymers that have demonstrated far-reaching utility biomaterials for use in many medical applications. Biodegradable elastomers can be broadly classified into networks prepared by either step-growth or chain-growth polymerization. Each processing strategy affords distinct advantages in terms of capabilities and resulting properties of the network. This work describes the synthesis, processing, and characterization of cross-linked polyester networks based on Diels-Alder coupling reactions. Hyperbranched furan-modified polyester precursors based on poly(glycerol-co-sebacate) are coupled with bifunctional maleimide cross-linking agents. The chemical and thermomechanical properties of the elastomers are characterized at various stages of network formation. Experimental observations of gel formation are compared to theoretical predictions derived from Flory-Stockmayer relationships. This cross-linking strategy confers unique advantages in processing and properties including the ability to fabricate biodegradable reconfigurable covalent networks without. additional catalysts or reaction byproducts. Reconfigurable biodegradable networks. Using Diels-Alder cycloaddition reactions permit the fabrication of shape-memory polymers with complex permanent geometries. Biodegradable elastomers based on polyester networks with molecular reconfigurability achieve vastly expanded properties and processing capabilities for potential applications in medicine and beyond.