The main reason for using mathematical models and diagrams in trade studies is to provide estimates of system effectiveness, performance or technical attributes, and cost from a set of known or estimable quantities. Typically, a collection of separate models is needed to provide all of these outcome variables. The heart of any mathematical model is a set of meaningful quantitative relationships among its inputs and outputs. These relationships can be as simple as adding up constituent quantities to obtain a total, or as complex as a set of differential equations describing the trajectory of a spacecraft in a gravitational field. Ideally, the relationships express causality, not just correlation. Furthermore, key to successful systems engineering activities are also the methods with which these models are efficiently and effectively managed and used to simulate the systems. However, diverse domains often present recurring problems of modeling and simulation for systems engineering, and new advancements are aiming to crossfertilize methods among distinct scientific and engineering communities, under the title of 'Modeling & Simulation-based Systems Engineering'.