Pseudo maximum likelihood techniques are applied to basic Poisson models and to Poisson models with specification errors. In the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p.d.f. of the disturbances. These estimators are compared both from the finite sample and the asymptotic point of view. Quasi generalized PML estimators, which asymptotically dominate all PML estimators, are also proposed. Finally, bivariate and panel data Poisson models are discussed.