Diagram algebras like the Temperley-Lieb algebra, Brauer algebra, and partition algebra are easy to explain by pictures and come up in various settings as Schur-Weyl duality, statistical mechanics, or knot theory. They have many similarities to the group algebra of the symmetric group, in particular, they are often semisimple and their irreducible representations are indexed by partitions. In this talk, I will introduce these algebras and their representation theory, and then explore sequences of representations, define the notion of representation stability for them, and give a categorical criterion for this notion. Speaker(s): Peter Patzt (University of Oklahoma)