This paper is a theoretical analysis of the consequences of workplace discrimination. We prove that discrimination against a group at lower levels of the hierarchy affects the pay of members of the same group at higher levels, leading to a "pay gap" relative to non-discriminated workers. These spillovers in turn induce firms to alter the match between workers and jobs for the discriminated group, potentially leading to a "glass ceiling". The phenomenon can occur even in firms where "equal pay for equal jobs" appears to be adhered to. The explanation is based on the standard participation and incentive constraints: the need to compensate workers for the direct discrimination they suffer, to induce them to work, and the need to maintain pay differentials between job levels, to provide effort incentives. We end the paper showing that neither competition among workers, nor competition among firms for workers eliminates these spillovers.