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This chapter contributes to ongoing debates about approaches to modeling student learning. By providing a basis for individual diagnoses, such models can foster teaching that is responsive to students' learning needs. In addition, these models can inform the development of standards and curricula and advance theory and research about student learning. This chapter highlights two approaches to modeling student learning: learning progressions (from the United States) and competence models (from German-speaking contexts). Taking into account the cultural context of both approaches, we identify similarities and differences with regard to selected criteria: kinds of models, model structure, application to teaching and learning, and evaluation through research. We illustrate our comparisons using a learning progression and a competence model describing students' learning about models and modeling in science education. The use of learning progressions and competence models in their respective contexts, for both research and practice, suggests that there are important insights that researchers from each tradition can learn through deeper understanding of the other in order to explore and foster student learning. Our efforts to clarify the meaning and contributions of the two approaches, with respect to each other, will help to foster communication across the international science education community. [For the complete volume, "Bridging Research and Practice in Science Education: Selected Papers from the ESERA 2017 Conference. Contributions from Science Education Research. Volume 6," see ED615249.]