Among the several areas of Statistics that have witnessed foundational contributions by the Italian community, a remarkable one relates to the development and study of tractable classes of skewed distributions. These families arise from the very elegant and practical idea of perturbing symmetric densities through a skewness–inducing mechanism that preserves tractability of the resulting class of distributions. As such, these families have been widely and successfully adopted in the design of statistical models for skewed phenomena. This short article aims at clarifying that the impact of skewed distributions goes even beyond the specification of effective likelihoods. In fact, within these families it is possible to identify (i) the conjugate priors for a broad variety of core statistical models often employed in practice (i.e., linear regression, probit, tobit, and multinomial probit), and (ii) novel limiting laws for generic posterior distributions that substantially improve the rate of convergence, and hence the approximation accuracy, relative to those provided by the classical Gaussians from the Laplace method. Such results are presented in this short article through a summary of the contributions by [1, 15, 16, 18, 20].