Stable random variables are the r.v.s that retain their shape when added together. These distributions generalize the Gaussian distribution and allow skewness and heavy tails - features found in many large data sets from finance, telecommunication and hydrology. We give an overview of univariate and multivariate stable laws, focusing on statistical applications. Examples of financial and other data sets will be given. These distributions are now computationally accessible and should be added to the toolbox of the working statistician.