The discovery of the proton-radius puzzle and the subsequent deuteron-radius puzzle is fueling an on-going debate on possible explanations for the difference in the observed radii obtained from muonic atoms and from electron-nucleus systems.
Atomic nuclei have a complex internal structure that must be taken into account when analyzing experimental spectroscopic results. {\it Ab initio} nuclear structure theory provided the so far most precise estimates of important corrections to the Lamb shift in muonic atoms and is well poised to also investigate nuclear structure corrections to the hyperfine splitting in muonic atoms. Independently on whether the puzzle is due to beyond-the-standard-model physics or not, nuclear structure corrections are a necessary theoretical input to any experimental extraction of electric and magnetic radii from precise muonic atom measurements.

Here, we review the status of the calculations performed by the TRIUMF-Hebrew University group, focusing on the deuteron, and discuss preliminary results on magnetic sum rules calculated with two-body currents at next-to-leading order. Two-body currents will be an important ingredient in future calculations of nuclear structure corrections to the hyperfine splitting in muonic atoms.