Methods for qualitative simulation allow predictions to be made on the behavior of a system for which no quantitative information is available. In addition, they help obtain a comprehension of the range of possible qualitative behaviors compatible with the structure of a system. This report reviews QSIM and other qualitative simulation methods. It discusses two problems that have seriously compromised the application of these methods to realistic problems in science and engineering: the occurrence of spurious behavior predictions and the combinatorial explosion of the number of behavior predictions. In response to these problems, related approaches for the qualitative analysis of dynamical systems have emerged: qualitative phase space analysis and semi-quantitative simulation. The report argues for a synthesis of these approaches to obtain a computational framework for the qualitative analysis of dynamical systems. This should provide a solid basis for further upscaling and for the development of model-based reasoning applications of a wider scope.