Exponential attractors of infinite dimensional dynamical systems are compact, semi-invariant sets of finite fractal dimension that attract all bounded subsets at an exponential rate. They contain the global attractor and, due to the exponential rate of convergence, are generally more stable under perturbations than global attractors. In the autonomous setting, exponential attractors have been studied for several decades and their existence has been shown for a large variety of dissipative equations. More recently, the theory has been extended to non-autonomous and random problems. We discuss general existence results for exponential attractors for nonautonomous and random dynamical systems in Banach spaces and derive explicit estimates on their fractal dimension. As an application semilinear heat and semilinear damped wave equations are considered. This is joint work with Tomas Caraballo (University of Sevilla) and Alexandre Carvalho (University of São Paulo).