Current understanding of what constitutes work in the growing gig economy is heavily conflated, ranging from conceptualisations of independent contracting to other forms of contingent labour. This article calls for a move away from problematic aggregations by proposing a classification of gig work into three variants, all based strongly upon key technological features: app‐work, crowdwork, and capital platform work. Focusing specifically on the app‐work variant, this article's more delineated focus on the textured dimensions of this work proposes new lines of enquiry into employment relationships and human resource management. Examining the crucial role of algorithmic management, we critically discuss the impact of this novel mediation tool used by gig organisations for the nature of employment relations within app‐work, work assignment processes, and performance management. In so doing, we propose a series of research questions that can serve as a guide for future research in this increasingly important field.