The study of the long-time behavior of solutions to nonautonomous differential equations from the point of view of a dynamical system can be based on the notion of a pullback attractor, which plays a similar role as the global attractor in autonomous dynamical systems. In this lecture I will present this notion and variations of its definition. Moreover, I will formulate the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result will be given in the context of the smoothing properties of the process and for pullback attractors attracting a given universe, i.e., a chosen class of possibly time-dependent families of sets. An application of the result to nonautonomous reaction-diffusion equations will be also presented.