Magnetic models with strong disorder are the topic of this work. Diluted antiferromagnets in an external field (DAFF) are of special interest, both from a theoretical, and from an experimental point of view. In this work critical exponents at various points in the temperature vs. magnetic field phase diagram are determined by the analysis of exact calculated ground states and of Monte Carlo simulations. The specific heat and its critical exponent deserve special attention. Simulations of irreversibilities of the specific heat are in agreement with latest measurements. Further emphasis is put on the investigation of the non-equilibrium dynamics of the DAFF. The relaxation dynamics of the DAFF is governed by thermal activation. Further it is shown that also the DAFF exhibits Aging effects, as they are known from many other disordered systems