In organizational research, studying "processes" is important for uncovering and understanding the underlying causal mechanisms in a predictor-mediator-outcome logic. Processes answer "how" and "why" questions and provide more complete explanations about phenomena. Our focus in this review is on studies of leadership processes, which we systematically analyze to report on the state-of-the science. In doing so, we present a two-dimensional target-centric taxonomy to integrate previous research: The taxonomy distinguishes the target's level (i.e., individual follower, team, organizational, and extra-organizational) as well as the type of leadership processes that affect either the target's development or leverage of resources. Our review indicates that the predominantly studied leadership "meta" process model looks at the effect of leader traits or behaviors on performance-related outcomes through cognitive, affective, or behavioral leveraging factors. This "meta" model points to several important and understudied processes including a leader's influence on the target's development or work context. We also identify two largely overlooked yet critical issues for leadership process research: Modeling the role of time and that of multiple processes through which leadership effects manifest themselves in organizations. Using our taxonomy, we provide several reflection points that can guide the development of genuine and thoughtful leadership process theories. We conclude by urging future leadership process research to embrace multi-process, multi-level, and time-sensitive models.