Online labor platforms (OLPs) can use algorithms along two dimensions: matching and control. While previous research has paid considerable attention to how OLPs optimize matching and accommodate market needs, OLPs can also employ algorithms to monitor and tightly control platform work. In this paper, we examine the nature of platform work on OLPs, and the role of algorithmic management in organizing how such work is conducted. Using a qualitative study of Uber drivers’ perceptions, supplemented by interviews with Uber executives and engineers, we present a grounded theory that captures the algorithmic management of work on OLPs. In the context of both algorithmic matching and algorithmic control, platform workers experience tensions relating to work execution, compensation, and belonging. We show that these tensions trigger market-like and organization-like response behaviors by platform workers. Our research contributes to the emerging literature on OLPs.