Since digital opportunities will continue altering business models, organizations need to formulate and execute digital strategies to sustain long-term value. A digital strategy is governed by the organization’s board. A board consists of executive and non-executive members, whereas in a two-tier system, the non-executive members form a supervisory board that is decoupled from the executive board. We present a framework illustrating how the actions of supervisory board members might influence digital strategy. We developed this framework based on a structured literature review with insights from corporate governance, strategic management, and board-level IT governance. We found that supervisory board members execute a variety of actions to take and shape strategic decisions and shape the strategic content, context, and conduct within their organization. We integrated our findings into sixteen potential actions that supervisory board members can take to influence digital strategy formulation, execution, and context. Further research should evaluate the framework and investigate the impact of their actions on digital strategies.