The equations governing the dynamics of a quantum vortex have been debated for nearly 50 years. We believe we have now solved this problem. The problem is not just a technical one – it has important experimental ramifications, and some very interesting physical ideas come out of the discussion. Part of the difficulty arises because phonons around an unscreened vortex have their wave-functions altered in a very basic way – they are not the same phonons. The problem has certain formal analogies with phenomena in General Relativity, and this analogy leads to very interesting physical insights. The new equation of motion contains non-local terms, which have strong effects at low temperatures. This lecture will be non-technical, and will focus on the physical ideas, as well as on the experimental consequences. Possible experimental tests will also be outlined.