Hierarchy is a reality of group life, for humans as well as for most other group-living species. And yet, there remains considerable debate about whether and when hierarchy can promote group performance and member satisfaction. We suggest that progress in this debate has been hampered by a lack of clarity about hierarchy and how to conceptualize it. Whereas prevailing conceptualizations of hierarchy in the group and organization literature focus on inequality in member power or status (i.e., centralization or steepness), we build on the ethological and social network traditions to advance a view of hierarchy as cascading relations of dyadic influence (i.e., acyclicity). We further suggest that hierarchy thus conceptualized is more likely to capture the functional benefits of hierarchy whereas hierarchy as inequality is more likely to be dysfunctional. In a study of 75 teams drawn from a wide range of industries, we show that whereas acyclicity in influence relations reduces conflict and thereby enhances both group performance and member satisfaction, centralization and steepness have negative effects on conflict, performance, and satisfaction, particularly in groups that perform complex tasks. The theory and results of this study can help to clarify and advance research on the functions and dysfunctions of hierarchy in task groups.