We provide an overview of the problem of jointly testing two hypotheses and estimating a parameter of the selected model. Such problems arise in a variety of applications. First, we present a conceptual introduction to suboptimal and optimal procedures for joint detection and estimation. A numerical example illustrates the advantages of the optimal procedure over suboptimal ones. Next, we discuss how more advanced problem formulations affect the presented results. The second part covers joint detection and estimation in a sequential framework. First, we provide an introduction to sequential analysis through sequential hypothesis testing. Then, suboptimal and optimal sequential procedures for joint detection and estimation are discussed. A numerical example shows the advantages of optimal sequential procedures over suboptimal and optimal sequential procedures with a fixed number of samples. The third part discusses open problems and future research directions in joint detection and estimation.

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