Analogy has returned to prominence in the field of inflectional morphology as a basis for new explanations of inflectional productivity. Here we review the rising profile of analogy, identifying key theoretical and methodological developments, areas of success, and priorities for future work. In morphological theory, work within so-called abstractive approaches places analogy at the center of productive processes, though significant conceptual and technical details remain to be settled. The computational modeling of inflectional analogy has a rich and diverse history, and attention is now increasingly directed to understanding inflectional systems through their internal complexity and cross-linguistic diversity. A tension exists between the prima facie promise of analogy to lead to new explanations and its relative lack of theoretical articulation. We bring this to light as we examine questions regarding inflectional defectiveness and whether analogy is reducible to grammar optimization resulting from simplicity biases in learning and language use.