While the very word “antigravity” is anathema to most scientists, this hasn’t stopped a few of them taking a speculative look at the subject, usually under euphemistic labels such as mass modification or gravity control. A recurring theme in this chapter, introduced at the start, is the notion—originating with Michael Faraday—that extensions to gravitational theory might be discovered by exploring its analogues in other branches of physics. We also take a brief look at Einstein’s theory of General Relativity, which—due to its fundamentally geometric nature—offers little prospect of antigravity in a practical sense, although it does predict exotic effects in areas like cosmology and black hole theory that could go by that name. Next we look at the topic of inertial mass—both theoretical explanations of it, and its practical implications for “reactionless” space drives and similarly advanced technology. This leads into a broader discussion of the exciting-sounding, but not always hugely productive, “breakthrough physics” research that has been carried out by the US Air Force, NASA and various private aerospace companies.