This thesis is concerned with the study of distributional and inferential aspects of some classes of flexible distributions used for modelling asymmetric data. In the last couple of decades, a great effort has been devoted to proposing new dis- tributions that can capture departures from normality. A popular method to obtain such distributions consists of adding parameters to a known, typically symmetric, distribution. In order to do so, several classes of parametric transformations have been employed. In Chapter 2, we analyse two families of such transformations that have recently been recom- mended as skewing mechanisms. We show that when they are applied to several symmetric distributions, the resulting models are not flexible enough to capture moderate or high skew- ness. Our aims here are to show that not every parametric transformation can be used as a skewing mechanism and to emphasise the importance of assessing the flexibility of a transformed distribution using interpretable measures of skewness. In Chapters 3–5, we focus on the study of univariate three-parameter location-scale models, where skewness is introduced by differing scale parameters either side of the loca- tion. This class of distributions is often termed two-piece distributions. We first present an application of a particular distribution of this kind in the context of microbiology. There, we propose a benchmark prior using the interpretability of the parameters of such model. Motivated by the importance of noninformative priors for practitioners, we then proceed to study the use of the Jeffreys prior in two-piece models and investigate the existence of the corresponding posterior distributions. We also propose a benchmark prior structure that produces proper posteriors under mild conditions for a wide class of two-piece models. In a second application, in the context of stress-strength models, we explore a bivariate ex- tension of two-piece distributions using copulas. There, we also propose Bayesian models based on the interpretation of the parameters. In Chapter 6, we introduce a five-parameter class of distributions obtained by vary- ing both scale and shape parameters on each side of the mode. We study several aspects of this sort of models such as: subfamilies of distributions, reparameterisations, interpretation of the parameters, and two multivariate extensions. We also propose benchmark priors and illustrate their use with real data. We compare the performance of these models against appropriate competitors using several criteria.