Sofic and hyperlinear groups generalise both residually finite and amenable groups, and the concept of soficity (or, more generally, embeddability into ultraproducts of finitary objects in the theory you study) is central to many important results and conjectures in measured group theory and operator algebras. In this talk, I will define sofic and hyperlinear groups and explain the interconnections between these notions and various other approximation properties of groups, graphs ajn operator algebras.