Polyesters carrying polar main-chain ester linkages exhibit distinct material properties for diverse applications and thus play an important role in today's plastics economy. It is anticipated that they will play an even greater role in tomorrow's circular plastics economy that focuses on sustainability, thanks to the abundant availability of their biosourced building blocks and the presence of the main-chain ester bonds that can be chemically or biologically cleaved on demand by multiple methods and thus bring about more desired end-of-life plastic waste management options. Because of this potential and promise, there have been intense research activities directed at addressing recycling, upcycling or biodegradation of existing legacy polyesters, designing their biorenewable alternatives, and redesigning future polyesters with intrinsic chemical recyclability and tailored performance that can rival today's commodity plastics that are either petroleum based and/or hard to recycle. This review captures these exciting recent developments and outlines future challenges and opportunities. Case studies on the legacy polyesters, poly(lactic acid), poly(3-hydroxyalkanoate)s, poly(ethylene terephthalate), poly(butylene succinate), and poly(butylene-adipate terephthalate), are presented, and emerging chemically recyclable polyesters are comprehensively reviewed.