Process tracing is a fundamental tool of qualitative analysis. This method is often invoked by scholars who carry out within-case analysis based on qualitative data, yet frequently it is neither adequately understood nor rigorously applied. This deficit motivates this article, which offers a new framework for carrying out process tracing. The reformulation integrates discussions of process tracing and causal-process observations, gives greater attention to description as a key contribution, and emphasizes the causal sequence in which process-tracing observations can be situated. In the current period of major innovation in quantitative tools for causal inference, this reformulation is part of a wider, parallel effort to achieve greater systematization of qualitative methods. A key point here is that these methods can add inferential leverage that is often lacking in quantitative analysis. This article is accompanied by online teaching exercises, focused on four examples from American politics, two from comparative politics, three from international relations, and one from public health/epidemiology.