Description: This paper discusses a class of asymmetric distributions arising in a random summation scheme. Members of the class are called asymmetric Laplace distributions as the standard Laplace distributions, which are symmetric, constitute a proper subclass. Among distributions which are limits in random summation schemes, asymmetric Laplace distributions play an analogous role to that of normal distributions among distributional limits of non-random sums. Asymmetric LaPlace laws are more 'peaky' and have heavier tails than normal laws. They have stability properties and are convenient in applications, as their densities have explicit forms and estimation procedures are easily implemented. Anticipating increasing interest in this class of distributions, the authors present statistical tools which can be utilized in practice, including algorithms for simulation and estimation. They also discuss more general classes of distributions, where asymmetric Laplace distributions appear as special cases.