New York City's public specialized high schools have a long history of offering a rigorous, college preparatory education to the city's most academically talented students. Though immensely popular and highly selective, their policy of admitting students using a single entrance exam has raised questions about diversity and equity in access. In this paper, we provide a descriptive analysis of the "pipeline" from middle school to matriculation at a specialized high school, identifying group-level differences in application, admission, and enrollment. In doing so, we highlight potential points of intervention to improve access for underrepresented groups. Controlling for other measures of prior achievement, we find black, Hispanic, low-income, and female students are significantly less likely to qualify for admission to a specialized high school. Differences in application and matriculation rates also affect the diversity in these schools, and we find evidence of middle school "effects" on both application and admission. Simulated policies that offer admissions using alternative measures, such as state test scores and grades, suggest many more girls, Hispanics, and white students would be admitted under these alternatives. They would not, however, appreciably increase the share of offers given to black or low-income students.