This is a short introductory note to the texts of lectures presented at a Royal Society Discussion meeting held on 14-15 February 2005 and now published in this issue of Philosophical Transactions A. It contains a brief resumé of the papers in the order they were presented at the meeting. This issue contains the texts of all of the presentations except those of Christophe Salomon, on cold atom clocks and tests of fundamental theory, and Francis Everitt, on Gravity Probe B, which were, unfortunately, not available.