We present a state-of-the-art theoretical approach for computing bound-state energies in muonic atoms, incorporating improved quantum electrodynamics effects and nuclear polarization corrections with a systematic assessment of theoretical uncertainties. Our approach is based on a combination of the $Z\alpha$ expansion and the all-order formalism (Furry picture) optimized for the medium-mass range $(3\le Z\lesssim 30)$ and guided by the accuracy requirements of modern muonic spectroscopy experiments. These calculations are directly relevant to ongoing and forthcoming measurements aimed at extracting nuclear structure parameters, particularly nuclear-charge radii, with unprecedented precision.

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• Atomic & molecular structure
• Electronic structure of atoms & molecules
• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions