The mathematics of quantum toroidal algebras is remarkably rich, and so are their applications to physics. These algebras and their representation theory arise in the mathematics of high-energy physics, string theory and supersymmetric gauge theories. They also play an important role in the analysis of central models in condensed matter physics, stochastic interacting particle systems and integrable probability. ACEMS researchers contribute to quantum toroidal algebras, which are quantum versions of toroidal Lie algebras.