Temperley-Lieb algebras are certain finite-dimensional algebras coming originally from statistical physics and knot theory. Around 2019, they became one of the first examples of homological stability for algebras, when Boyd and Hepworth showed that in low dimensions the homology vanishes. I will explain what we mean by homology of an algebra, and then explain what we know about this problem. We're now able to give some complete calculations of the homology, which has a surprisingly rich structure. This is joint work in progress with Rachael Boyd, Oscar Randal-Williams, and Robin Sroka. Prerequisites will be minimal.