In this thesis, the hydrodynamic limit (HDL) for two trapping models is studied, the Random Waiting Time Model (RWTM) and the fractional kinetics process (FKP), on a discrete lattice Zd . The RWTM is studied for dimension d ≥ 1 and E[wi ],∞where wi denotes the waiting time at position i . On the other hand, the FKP is studied for d ≥ 3 and a nonexisting first finite moment. Instead, it is assumed that the waiting times wi follow a power law distribution. Two main results are presented in this thesis. Firstly, it is proven that the HDL for the RWTMconverges to the solution of the heat equation. The solution is deterministic. The proof consists of showing that the expectation value of the empirical density fields converge to the aforementioned solution by using the duality property and Doob’s theorem, and that the variance is finite and decays to 0. Additionally, it is proven that a rescaled random walk converges to a Brownian motion by using Lévy’s characterisation of Brownianmotion. Secondly, it is proven that the HDL for the FKP converges to a random measure of the solution of the fractional heat equation, defined in the Caputo sense. Hence, the solution is random. The proof consists of using similar techniques of the proof of the RWTM and of using that the limit of a sequence of random speed measures is again random. Before all of this, an introduction toMarkov processes, their semigroups, martingales, and generators is presented. Additionally, an introduction to random walks, Brownianmotion, and duality is included.