Methods for qualitative simulation allow predictions on the dynamics of a system to be made in the absence of quantitative information, by inferring the range of possible qualitative behaviors compatible with the structure of the system. This article 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 dynamic systems have emerged: qualitative phase-space analysis and semi-quantitative simulation. The article argues for a synthesis of these approaches in order to obtain a computational framework for the qualitative analysis of dynamic systems. This should provide a solid basis for further upscaling and for the development of model-based reasoning applications of a wider scope.