In 1985, skew-normal distribution was articulated, which modifies the normal probability density function by a multiplicative skewing function, and since then the idea has been extended to elliptically contoured distributions, yielding various families of skew-elliptical distributions. Contributors from around the world review the current state of the art and describe new developments, reporting theoretical results and applications previous scattered throughout the literature. Among the 20 topics are elliptical models subject to hidden truncation or selective sampling, and skewed link models for categorical response data.