Prior to 1988, traversable wormholes were just science fiction. Prior to 1994, warp drives were just fiction. Since then, these notions matured into published scientific discourse, where key issues and unknowns continue to be raised and investigated. In 2009, the American Institute of Aeronautics and Astronautics published a peer-reviewed, expansive technical volume on these and other investigations toward breakthrough propulsion. This paper summarizes the key assertions from that 739-page volume, describing the collective state-of-the-art and candidate research steps that will lead to discovering if, or how, such breakthroughs might finally be achieved. Coverage includes: prerequisites for space drive physics, manipulating gravity or inertia for propulsion, lessons from superconductor experiments, null results with "lifters", implications of photon momentum in media, quantum vacuum physics, and the faster-than-light implications of general relativity and quantum non-locality.