Abstract: The existence of bias in inferential procedures based on the likelihood function has given rise to a great deal of research in the statistical literature. This is a matter of serious concern when the available sample size is small to moderate or when the model under study does not meet the regularity conditions for usually reliable maximum likelihood inference. In this talk, we discuss the impact of bias in both these circumstances. For finite-sample problems, we suggest one convenient way to refine Wald-type inference in regression settings through asymptotic bias correction of the z-statistic. For non-regular problems, with special focus on scenarios characterized by the presence of incidental parameters, we suggest a Monte Carlo strategy to extend the current range of applications of the modified profile likelihood.