The term “Breakthrough Propulsion Physics” comes from the NASA project by that name which examined non-rocket space drives, gravity control, and faster-than-light travel. The focus here is on space drives and the related unsolved physics of inertial frames. A “space drive” is a generic term encompassing any concept for using as-yet undiscovered physics to move a spacecraft instead of existing rockets, sails, or tethers. The collective state of the art spans mostly steps 1–3 of the scientific method: defining the problem, collecting data, and forming hypotheses. The key issues include (1) conservation of momentum, (2) absence of obvious reaction mass, and (3) the net-external thrusting requirement. Relevant open problems in physics include: (1) the sources and mechanisms of inertial frames, (2) coupling of gravitation to the other fundamental forces, and (3) the nature of the quantum vacuum. Rather than following the assumption that inertial frames are an immutable, intrinsic property of space, this paper revisits Mach's Principle, where it is posited that inertia is relative to the distant surrounding matter. This perspective allows conjectures that a space drive could impart reaction forces to that matter, via some as-yet undiscovered interaction with the inertial frame properties of space. Thought experiments are offered to begin a process to derive new hypotheses. It is unknown if this line of inquiry will be fruitful, but it is hoped that, by revisiting unsolved physics from a propulsion point of view, new insights will be gained.