We discuss two different limits where correlated lattice fermions are explicitly tractable: that of infinite range hopping and that of high dimensions. While in the first case results are almost trivial, the latter limit turns out to be particularly significant, since in d=∞ theoretical investigations are enormously simplified, while at the same time correlations remain non-trivial. Contact to finite dimensions can be made via systematic 1/d-expansions. We review the state-of-art of this approach.