Matter in neutron star cores reaches extremely high densities, forming states of matter that cannot be generated in the laboratory. The Equation of State (EOS) of the matter links to macroscopic observables, such as mass M and radius R, via the stellar structure equations. A promising technique for measuring M and R exploits hotspots (burst oscillations) that form on the stellar surface when material accreted from a companion star undergoes a thermonuclear explosion. As the star rotates, the hotspot gives rise to a pulsation, and relativistic effects encode information about M and R into the pulse profile. However the burst oscillation mechanism remains unknown, introducing uncertainty when inferring the EOS. I review the progress that we are making towards cracking this long-standing problem, and establishing burst oscillations as a robust tool for measuring M and R. This is a major goal for future large area X-ray telescopes.