Sociologists theorize race as a socially constructed process telling us about participation in social relations of domination, but often treat race as an essential trait telling us about a person. This treatment obscures social processes that constitute racial systems. In this dissertation, I examine racial classification, moments when an individual is racially classified by another person as though they belong to a certain racial group. As longitudinal data presenting racial classification changes challenge the treatment of race as an essential trait, researchers often interpret these data as measurement error, rather than racial reclassifications. I begin by asking if racial classification change data present measurement error or if they reveal racial reclassification. I test which conception of race—essential trait or social relation—best supports analyses of a sample of racial classification events occurring in the National Longitudinal Survey of Youth, 1997 (NLSY97). Employing Generalized Linear Mixed Models (GLMMs), I found that racial classification changes occur in predictable ways that indicate they should not be understood as measurement error. This work contributes to the study of race by opening up processes of racial formation to direct quantitative analysis. It also offers empirical evidence to evaluate theories of Latin Americanization of the U.S. racial system. I then directly examined Latino racialization in the U.S. by analyzing what factors predict how self-identified Latinos are racially classified using NLSY97 panel data. Results of GLMMs suggest that upward or downward socioeconomic mobility predicts racial classification as white or non-white, respectively, for self-identified Latinos. My results underscore challenges to studying the socioeconomic incorporation of Latinos in the U.S. and suggest ways that the racial composition of the U.S. population may be changing. Last, I examined how people who are racially classified as white are ethnically classified by others as Latino or not Latino in the U.S. Results of GLMMs suggest that the way a person is ethnically classified tells us something dynamic about their position in a social hierarchy. This research suggests ways that racialized ethnic classification as Latino complicates racial classification as white.