The understanding of the asymptotic behaviour of dynamical systems is one of the most important problems of modern mathematical physics. One way to treat this problem for systems having some dissipativity properties is to analyze the existence and structure of its global attractor. On some occasions, some phenomena are modelled by nonlinear evolutionary equations which do not take into account all the relevant information of the real systems. Instead some neglected quantities can be modelled as an external force which in general becomes time-dependent. For this reason, non-autonomous systems are of great importance and interest. Several models of reaction-diffusion equations in bounded and unbounded domains are analyzed in this book. Using the pullback theory so much for single-valued as for multi-valued non-autonomous dynamical systems, since this allows for more generality in the non-autonomous terms, the existence of pullback attractors for our models of reaction-diffusion equations is proved in this book.