The use of algorithms to manage human resources represents one of the most significant recent developments in HRM research and practice. While harboring the potential to facilitate more efficient and accurate HR processes, the emergence of algorithmic HRM also raises concerns for workers operating under advanced data-driven systems. Currently, algorithmic HRM is most prevalent in labor markets in the gig economy, and particularly in localized, app-based forms of gig work. In this paper, we adopt a qualitative research design to examine how gig workers in both the food-delivery and rideshare sectors react to the dynamic features of algorithmic HRM practice. In doing so, we explore how these reactions positively and/or negatively impact on the work arrangement and reveal the key concerns and issues encountered by workers operating under algorithmic HRM systems. We find that gig workers grow frustrated and disillusioned as they navigate the constraints of algorithmic HRM, and that workers may adopt informal and individual efforts to reclaim aspects of their autonomy. Where these efforts failed, workers exhibited disruptive behaviours and resistance to the pervasive and heavily prescriptive algorithmic HRM features encountered. The role that other non-organizational actors can play in this is notable.