We consider Conformal Field Theories perturbed by quenched disorder. Such systems often flow to new, disordered, fixed points of the renormalization group. For the Ising model in d = 3 with random bonds, we calculate some properties of the disordered fixed point in perturbation theory in the heat capacity exponent. We compare with experimental data. The two methods that we use are an approximation around the pure 3d Ising model and an \epsilon expansion around d=2. We further analyze several aspects of large-N disordered theories. A natural large-N limit of theories with disorder is identified. We find a nontrivial generalization of the Imry-Ma instability. The beta functions at large N can be computed exactly. The presence of double trace operators changes the heat capacity exponent expansion in a qualitative fashion. We solve a class of disordered large-N theories and find the new critical exponents.