The cost of attending college has risen sharply over the last 40 years. Although more credit and grant aid have been made available to students, there are still major gaps between aid and the cost of attendance for many students in the United States, all of whom are left to figure out whether they can afford the remaining costs associated with attending college. Given that people with similar financial means may make different decisions about what they can and cannot afford to pay for college, it is difficult to identify a universal definition of affordability. Nevertheless, examining college cost, student financial need, and progress toward degree completion trends in concert with one another can help illuminate patterns of when college is unaffordable. This paper will develop a definition of college affordability by examining the literature on student financial need and student aid interventions as well as student data collected by MDRC to identify important indicators of college affordability and the lack thereof, which may ultimately help or impede college persistence and graduation. This paper provides a review of the literature on the relationships between unmet financial need and progress toward degree completion as well as a review of the findings from studies that show the effects of financial aid intervention on student persistence and completion. The paper then examines MDRC's experimental data from the Performance-Based Scholarship (PBS) Demonstration, a study spanning six states around the United States. Ultimately, this paper offers several puzzle pieces that fit together to help identify the students for whom college may not be affordable. It also offers recommendations for how policymakers in various sectors can respond to the affordability issues faced by the low-income students they serve and want to help to achieve success in college. [This paper was written with Melvin Gutierrez and Jessica Gingrich.]