In the first part, I will describe the existence of a Large Deviation Principle for free fermion systems subjected to external electric fields. After that, I will state that for weakly interacting fermions on the lattice, the logarithm moment generating function of probability distributions associated with KMS states can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform determinant bound and to be summable even in the disorder setting. Finally, I will discuss how to prove a Large Deviation Principle for current observables in the interacting setting.