Learning progressions (LPs) are hypothetical models of learning developed with the aim of informing the design of standards, curriculum, instruction, and assessment in K-16 settings. The promise of LPs to inform designs for learning across grades and grade bands is an attractive prospect to learning scientists, particularly in math and science, who seek to fundamentally change learning settings through design. LPs in science and mathematics share several core features. They are organized around a few core disciplinary ideas and practices and describe the development of students’ understandings as intermediate steps or levels of growing sophistication. Descriptions of these levels are grounded in research on student learning in the domain, and progress along the levels is mediated by targeted instruction and curriculum. LPs by their very nature are conjectural models of learning over time that need to be empirically validated. Examination of a variety of existing progressions shows that their core features can be operationalized in different ways. These features include (a) the scope of the progression, (b) the type of constructs (core ideas) included; (c) how progress along a progression is conceptualized; and (d) the methods used to develop and refine LPs. We discuss each of these features using examples drawn from science and mathematics progressions. We further examine concerns and criticisms of LPs raised in the literature, including issues of construct and consequential validity and some of the challenges with classroom and policy applications. We agree with many of the criticisms raised, particularly the importance of accounting for the complex, contextual, and nuanced nature of learning in LPs. We anticipate that this young field will continue to evolve, improve, and contribute to learning, teaching, assessment, and policy.