This book was written for the 2nd Annual Modeling and Simulation Summit, Pre-Conference Focus Day Workshop: Using Math to Defeat the Enemy: Combat Modeling for Simulation (Monday, August 29th 2011). Although mathematics is key to combat model for simulation, this book provides just a cursory survey of mathematical model, and includes heuristics and other algorithms. The book covers behavior models, environmental models, communication models, target detection models, attrition model, entity and aggregate level models, and multi-resolution models. It provides examples of past and current model, simulations, and wargames to stimulate learning and discussion.