Data from many applied fields exhibit both heavy tail and skewness behavior. For this reason, in the last few decades, there has been a growing interest in exploring parametric classes of asymmetric distributions. A popular approach to model departure from normality consists of modifying a symmetric probability density function introducing skewness. This allows to measuring the disparity of a particular probability density function from a normal one using information measures. In this monograph, these tools are studied to the full symmetric class of multivariate elliptical and skew-elliptical distributions, and related families. Specifically, the Shannon entropy and negentropy, Kullback¿Leibler and Jeffrey¿s divergences, and Jensen¿Shannon distance are developed for these distributions. Finally, the results are applied on several real data sets: a seismological catalogue related to the 2010 Maule earthquake, a optimal design of an ozone monitoring station network, and on biological catalogues of anchovy and swordfish from the coast of Chile.