The Internet of Things (IoT) is undeniably transforming the way that organizations communicate and organize everyday businesses and industrial procedures. Its adoption has proven well suited for sectors that manage a large number of assets and coordinate complex and distributed processes. This survey analyzes the great potential for applying IoT technologies (i.e., data-driven applications or embedded automation and intelligent adaptive systems) to revolutionize modern warfare and provide benefits similar to those in industry. It identifies scenarios where Defense and Public Safety (PS) could leverage better commercial IoT capabilities to deliver greater survivability to the warfighter or first responders, while reducing costs and increasing operation efficiency and effectiveness. This article reviews the main tactical requirements and the architecture, examining gaps and shortcomings in existing IoT systems across the military field and mission-critical scenarios. The review characterizes the open challenges for a broad deployment and presents a research roadmap for enabling an affordable IoT for defense and PS.