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Economics tends to define and measure discrimination as disparities stemming from the direct (causal) effects of protected group membership. But work in other fields notes that such measures are incomplete, as they can miss important systemic (i.e. indirect) channels. For example, racial disparities in criminal records due to discrimination in policing can lead to disparate outcomes for equally-qualified job applicants despite a race-neutral hiring rule. We develop new tools for modeling and measuring both direct and systemic forms of discrimination. We define systemic discrimination as emerging from group-based differences in non-group characteristics, conditional on a measure of individual qualification. We formalize sources of systemic discrimination as disparities in signaling technologies and opportunities for skill development. Notably, standard tools for measuring direct discrimination, such as audit or correspondence studies, cannot detect systemic discrimination. We propose a measure of systemic discrimination based on a novel decomposition of total discrimination--disparities that condition on underlying qualification--into direct and systemic components. This decomposition highlights the type of data needed to measure systemic discrimination and guides identification strategies in both observational and (quasi-)experimental data. We illustrate these tools in two hiring experiments. Our findings highlight how discrimination in one domain, due to either accurate beliefs or bias, can drive persistent disparities through systemic channels even when direct discrimination is eliminated