This Article investigates the important, and often overlooked, structure–property relationships underlying the complex viscoelastic and adhesion behaviors of soft polyester elastomers, an emerging class of degradable biomaterials with promising applications in industry, biotechnology, and medicine. A family of poly(isosorbide fatty alkylates) with different molecular architectures and physical aspects (viscous, sticky, rubbery, solid) is reported. We demonstrate that the adhesiveness of these materials can be mainly understood in terms of bulk viscoelasic factors, in contrast to alternative ideas reported in the literature. These results shed some light on the intimate structure of bioelastomers, and notably on the decisive role of a well-adjusted macroscopic cluster of percolated polyester chains for tailoring key biomaterial functions such as elasticity, stickiness, fibrillation, and biodegradation. By establishing a bridge between polyester biomaterials and the material science of sticky things, this Article provides robust design principles for diverse functional biomaterials with tailored dissipative characters such as adhesives with tunable stickiness and degradation profiles, or scaffolds mimicking the nonlinear elasticity of supersoft biological tissues.