Close monitoring of vital physiological parameters is often key in following the evolution of certain medical conditions (e.g., diabetes, infections, post-operative status or post-traumatic injury). The allocation of trained medical staff and specialized equipment is, therefore, necessary and often translates into a clinical and economic burden on modern healthcare systems. As a growing field, transient electronics may establish fully bioresorbable medical devices capable of remote real-time monitoring of therapeutically relevant parameters. These devices could alert remote medical personnel in case of any anomaly and fully disintegrate in the body without a trace. Unfortunately, the need for a multitude of biodegradable electronic components (power supplies, wires, circuitry) in addition to the electrochemical biosensing interface has halted the arrival of fully bioresorbable electronically active medical devices. In recent years molybdenum (Mo) and tungsten (W) have drawn increasing attention as promising candidates for the fabrication of both energy-powered active (e.g., transistors and integrated circuits) and passive (e.g., resistors and capacitors) biodegradable electronic components. In this review, we discuss the latest Mo and W-based dissolvable devices for potential biomedical applications and how these soluble metals could pave the way towards next-generation fully transient implantable electronic systems.