Diagram algebras - what are they good for?

In this talk, I will introduce the audience to diagram algebras and their numerous connections to other areas of mathematics and mathematical physics. We will discuss the appearance of diagram algebras in statistical physics (loop models, Potts models), quantum group theory, combinatorics and stochastic processes on graphs. In particular, in the second half of the presentation, I will explain recent results on diagram algebras and their connection to random lattice paths and random walks on trees.