As the real-world use of Artificial intelligence (AI) becomes increasingly pervasive, the interest of organizations in the nascent technology is currently at its peak. Although the scientific literature points out that a strategy is key to responding to technological breakthroughs, the three facets of autonomy, learning, and inscrutability that distinguish contemporary AI from previous generations of IT give rise to a novel and distinctive perspective on strategy. Particularly, the facets of contemporary AI lead to AI-induced market and resource shifts and, thus, to AI-related strategic challenges regarding the scope, scale, speed, and source from which organizations make strategic deliberations. This ultimately requires a strategic response from organizations in the form of an AI strategy. Against this backdrop, this study proposes a multi-layer taxonomy with 15 dimensions and 45 characteristics that unveils how organizations currently structure and organize an AI strategy. Conducting a cluster analysis on this foundation, this study further provides four clusters that delineate predominant design options for developing a new AI strategy or evaluating an existing one. In this way, the results contribute to a fundamental understanding of the design space of an AI strategy and enrich recent discussions among researchers and practitioners on how to advance the real-world use of AI.