In order to illustrate what happens in specific models we will discuss three classes of models: the so-called 331 models, models with heavy vector-like quarks and models with leptoquarks, either of spin-0 or spin-1. We will concentrate on models with leptoquarks having sufficiently low masses so that they could be in principle discovered by the LHC. But even if the masses of new particles in the models considered will turn out to be beyond the reach of the LHC, their presence can still be identifiedin the rare processes discussed by us. These three classes of models are sufficiently simple so that we can present them here in some details. The new aspect of these models will be larger involvement of leptons than in previous sections. Yet, in thischapter we will confine the phenomenology to quark flavour observables postponing the discussion of lepton flavor violation to the next chapter. There are several more complicated models that we will only briefly mention providing list of references to papers investigatingweak decays in these models.