Qualitative reasoning is a collection of methods for building and simulating models of physical systems in spite of incomplete knowledge. The QSIM representation and simulation algorithm apply to models in the form of qualitative differential equations, which allow incompletely known quantity spaces and functional relations, and isolated behavioral discontinuities, to be described qualitatively. In the past few years, we have extended the early “limit analysis” methods for qualitative simulation to more sophisticated methods capable of simulating realistic systems. • The qualitative behavior description can be augmented and refined with incomplete quantitative information, producing more detailed predictions and detecting and excluding behaviors that are qualitatively plausible but quantitatively impossible. • The phase space representation, and the mathematical theory of dynamical systems, provides a more global perspective and more sophisticated filters on the set of qualitative predictions. • Complex systems must be hierarchically decomposed into simpler ones. In a time-scale abstraction hierarchy, fast mechanisms view slower mechanisms as constant, while slow mechanisms view faster ones as instantaneous (e.g. as functional relations). • Model-building methods based on device-centered and process-centered ontologies have been implemented as compilers which build qualitative differential equations for QSIM to simulate. • Applications of qualitative simulation are under development for monitoring and diagnosis of dynamic processes; and for recognizing and expressing teleological relationships in design.