The still undetermined equation of state of dense nuclear matter can be constrained by measuring the masses and radii of neutron stars. X-ray observations of rotation-powered millisecond pulsars (MSP) with NICER provide the phase-energy information necessary to apply the pulse-profile modelling technique and extract their mass and radius. ATHENA will also be enable such analyses with improved sensitivity, lower background, and more importantly, with a background that can be empirically determined. Nonetheless, a lot of complementary information can be obtained from soft and hard X-ray observations with current and future observatories. I think talk, I will show that the entire (warm) surface emission of MSPs can also help measure the neutron star radius. I will also discuss the possible contributions of non-thermal emission in the soft and hard X-ray band and how they may affect pulse-profile modelling. Finally, in the context of ATHENA observations of MSPs, I will discuss briefly how the high-resolution spectroscopy capabilities of X-IFU might reveal atomic and/or cyclotron spectral features. This would help characterising the surface gravity (redshifting the atomic lines) and/or the magnetic field structure and strength of MSPs