This article summarizes the continuous latent trait IRT approach to skills diagnosis as particularized by a representative variety of continuous latent trait models using item response functions (IRFs). First, several basic IRT-based continuous latent trait approaches are presented in some detail. Then a brief summary of estimation, model checking, and assessment scoring aspects are discussed. Finally, the University of California at Berkeley multidimensional Rasch-model-grounded SEPUP middle school science-focused embedded assessment project is briefly described as one significant illustrative application.