While it is often believed that the origins of life required participation of early biomolecules, it has been recently proposed that "non-biomolecules", which would have been just as, if not more, abundant on early Earth, could have played a part. In particular, recent research has highlighted the various ways by which polyesters, which do not participate in modern biology, could have played a major role during the origins of life. Polyesters could have been synthesized readily on early Earth through simple dehydration reactions at mild temperatures involving abundant "non-biological" alpha hydroxy acid (AHA) monomers. This dehydration synthesis process results in a polyester gel, which upon further rehydration, can assemble into membraneless droplets proposed to be protocell models. These proposed protocells can provide functions to a primitive chemical system, such as analyte segregation or protection, which could have further led to chemical evolution from prebiotic chemistry to nascent biochemistry. Here, to further shed light into the importance of "non-biomolecular" polyesters at the origins of life and to highlight future directions of study, we review recent studies which focus on primitive synthesis of polyesters from AHAs and assembly of these polyesters into membraneless droplets. Specifically, most of the recent progress in this field in the last five years has been led by laboratories in Japan, and these will be especially highlighted. This article is based on an invited presentation at the 60th Annual Meeting of the Biophysical Society of Japan held in September, 2022 as an 18th Early Career Awardee.