Machine-learning algorithms are deployed in an ever-growing array of selection processes, ranging from everyday applications like recommendations in online platforms, to high-stakes decisions in hiring, loans, and college admissions. These algorithms wield substantial influence over the level of exposure that candidates receive from decision-makers, and in turn their chances of selection. This dissertation investigates the fairness issue in the allocation of exposure among candidates within selection processes, encompassing screening processes, two-stage recommender systems, and multi-armed bandit problems. It identifies instances where conventional machine-learning approaches may be perceived as unfair, formulates fairness objectives to counter unfairness, and introduces machine-learning algorithms that implement these fairness objectives despite biases in the data and machine learning models, backed by theoretical guarantees. Beyond theoretical analysis, extensive empirical evaluations show the effectiveness of the proposed machine-learning algorithms in promoting fair allocation of exposure across a range of selection processes.