Using a unique dataset of 44 Massive Open Online Courses (MOOCs), this paper examines critical patterns of enrollment, engagement, persistence, and completion among students in online higher education. By leveraging fixed-effects specifications based on over 2.1 million student observations across more than 2,900 lectures, we analyze engagement, persistence, and completion rates at the student, lecture, and course levels. We find compelling and consistent temporal patterns: across all courses, participation declines rapidly in the first week but subsequently flattens out in later weeks of the course. However, this decay is not entirely uniform. We also find that several student and lecture-specific traits are associated with student persistence and engagement. For example, the sequencing of a lecture within a batch of released videos as well as its title wording are related to student watching. We also see consistent patterns in how student characteristics are associated with persistence and completion. Students are more likely to complete the course if they complete a pre-course survey or follow a quantitative track (as opposed to qualitative or auditing track) when available. These findings suggest potential course design changes that are likely to increase engagement, persistence, and completion in this important, new educational setting.