AbstractSpatially resolved studies of galaxies in the high-redshift Universe have traditionally been reliant on data at rest-frame optical and UV wavelengths, which can be biased towards the least dust-obscured galaxies. For several years now, we have been able to resolve and probe the morphology of longer-wavelength emission from distant galaxies with ALMA, and a number of recent ALMA studies were presented at the IAU Symposium No. 352. These included our study of the resolved multi-wavelength emission of galaxies at z ∼ 2. As part of the SHiZELS collaboration, we are mapping the Hα emission line (from SINFONI/VLT), UV continuum (from HST), and the far-infrared (from ALMA) emission from a small sample of Hα-selected galaxies. In this proceedings paper, we showcase the high quality of our data, and the spectacular structures displayed by one of our most dusty sources. We also provide an overview of some highly complementary simulation-based work, using galaxies drawn from the FIRE-2 zoom-in cosmological hydrodynamical simulations. Using sophisticated radiative transfer techniques, we have derived predictions for the spatially-resolved emission of a sample of star-forming galaxies, from rest-frame far-ultraviolet to the far-infrared. For both observed and simulated galaxies, emission maps show striking differences with wavelength, with the same galaxy appearing clumpy and extended in the far-ultraviolet yet compact at far-infrared wavelengths.