Used to be, they would loft a whole bunch of concentric cylinders, and rely on total internal reflection off their surfaces, which works even with X-rays.
If I understand correctly what they do now, they treat the diffraction pattern from X-rays going through a mask as a sort of 2-D Fourier transform, and transform it to an image with the inverse transform based on the known mask. Which is very clever. I don't doubt that this description glosses over the actually interesting bits.
The cylinder approach (actually paraboloid-hyperboloid or Wolter-I optics) is the main design used today and for future telescopes for lower energy X-rays. Focusing optics have a big advantage of having a lower level of background compared to a coded mask. Future Wolter-I optics use clever designs for the telescope, such as stacking silicon wafers into modules planned for the ESA Athena observatory [1] or modular lightweight single crystal silicon mirrors planned for future NASA missions [2].
Total internal reflection gets harder at higher energies since the angle of incidence has to be smaller, meaning a the effective area of the mirrors gets smaller. Once you get up to gamma ray energies, mirrors are not really feasible, and straight line optics like coded masks are the way to go.
The coded mask technology is really cool. The mask pattern is chosen in such a way that the inverse transform generates a unique solution (along with a whole lot of background noise that gets distributed more evenly and so can be subtracted out). Not to downplay that subtraction - modelling the noise in a coded mask system is one of the hardest parts of analysing the data. Worked on data from a coded mask mission once - 2 years to model the noise and correct for it, 6 months to do the science on the results.
