Thermogelling polymers belong to a class of stimuli-responsive hydrogels that undergo a macroscopic sol-to-gel transition in response to temperature. Much of the ongoing research in this field is focused on hydrogels for biomedical applications as an injectable sustained drug-release matrix or scaffolds for tissue regeneration. Despite robust developments in biodegradable thermogelling polymers in recent decades, the field still faces challenges in the optimization of materials properties. Thorough investigation must be performed to understand the effectiveness of drug delivery using hydrogel-forming polymer carriers. A highlighted case study on OncoGel, an experimental drug delivery depot formulation, sheds some light on the shortcomings of biodegradable thermogelling polymers as drug delivery systems. In this article, we highlight developments in biodegradable thermoresponsive polymers for biomedical applications over the past three years, with a focus on materials/technical challenges and the approaches used to resolve these problems.