Abstract: Homological stability is originally a property of (families of) groups, but recently, there has been a surge of interest in studying it for associative algebras too. Typically, the known results assert something stronger than stability, namely that 1) a certain family of group algebras includes into our family of algebras, and 2) this inclusion is a homology isomorphism in a range. Stability then follows from stability for the groups, if known. I'll start with an overview of the area, and discuss how these "stable identifications" of the homology often hold in a range exceeding the stability range. The main examples will be the Partition and Jones annular algebras.