This work was conceived as a logical sequel to Computer-Assisted Simulation of Dynamic Systems with Block Diagram Languages published by CRC Press in 1993. Its contents reflect suggestions, challenges and requests from academic, industrial, and military people in the U.S. and from around the world. The main objective of this book is two-fold: first to discuss the role of block languages as tools and to expose the technical features of several advanced languages. In the interest of diversity, we have selected ACSL/GM (Advanced Continuous Simulation Language/Graphic Modeller), ESL (European Space Agency Simulation Language), Extend, MATRIX[subscript x], SIMULINK, SystemView, TUTSIM (Twente University of Technology Simulation Language, U.S. version), and VisSim. Most of the time, languages are discussed alphabetically. These discussions revolve about the technical aspects of each language. There is no intent of product comparison - that is a reader's task. Secondly, we have included discussions on critical simulation-related topics and on material pertaining to special simulation demands and their solutions. . Our efforts toward the synthesis of an informative and self-contained book on block languages led to the inclusion of a review section on block diagram algebra and applied transfer functions. To reiterate a position of long standing, we believe that block diagram algebra is clearly a branch of mathematics and is necessary knowledge for those working in continuous dynamic system simulation.