Abstract: The Urnings rating system is an algorithm for tracking changes in ability and item difficulty in real time. When in equilibrium, the estimates are unbiased and their measurement error is known, which makes the system suitable for high-stakes testing. Furthermore, it is computationally very efficient, which makes it suitable for large-scale applications. The Urnings system has been successfully used on historic chess data, star ratings of movies by users, and data from ACT academy. However, until recently the applications of the system have been limited by the restrictiveness of the Rasch model that it is based on. In this presentation we describe the Urnings rating system and its properties, and extend it to a wide range of multidimensional models, including IRT models and CDMs.