As algorithmic systems increasingly shape workplace dynamics, human resource management (HRM) is undergoing a profound transformation. Algorithmic HRM – defined as the use of software algorithms to automate or augment HR-related decisions – offers potential gains in efficiency and objectivity across the different HRM processes. However, its implementation also raises critical concerns about fairness, transparency, worker autonomy and trust. This paper explores the defining features of algorithmic HRM, examines its implications for employee experiences, and analyses emerging risks. It concludes with a managerial toolkit for responsible algorithmic HRM, outlining reflective questions and strategies that HR professionals can use to align algorithmic practices with ethical standards, employee well-being, and organizational integrity.