We discuss the construction of probabilistic models centering on temporal patterns of query refinement. Our analyses are derived from a large corpus of Web search queries extracted from server logs recorded by a popular Internet search service. We frame the modeling task in terms of pursuing an understanding of probabilistic relationships among temporal patterns of activity, informational goals, and classes of query refinement. We construct Bayesian networks that predict search behavior, with a focus on the progression of queries over time. We review a methodology for abstracting and tagging user queries. After presenting key statistics on query length, query frequency, and informational goals, we describe user models that capture the dynamics of query refinement.