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The nebular recombination line H$\alpha$ is widely used as a star-formationrate (SFR) indicator in the local and high-redshift Universe. We present adetailed H$\alpha$ radiative transfer study of high-resolution isolatedMilky-Way and Large Magellanic Cloud simulations that include radiativetransfer, non-equilibrium thermochemistry, and dust evolution. We focus on thespatial morphology and temporal variability of the H$\alpha$ emission, and itsconnection to the underlying gas and star formation properties. The H$\alpha$and H$\beta$ radial and vertical surface brightness profiles are in excellentagreement with observations of nearby galaxies. We find that the fraction ofH$\alpha$ emission from collisional excitation amounts to $f_{\rmcol}\sim5-10\%$, only weakly dependent on radius and vertical height, and thatscattering boosts the H$\alpha$ luminosity by $\sim40\%$. The dust correctionvia the Balmer decrement works well (intrinsic H$\alpha$ emission recoverablewithin $25\%$), though the dust attenuation law depends on the amount ofattenuation itself both on spatially resolved and integrated scales. Importantfor the understanding of the H$\alpha$-SFR connection is the dust and heliumabsorption of ionizing radiation (Lyman continuum [LyC] photons), which areabout $f_{\rm abs}\approx28\%$ and $f_{\rm He}\approx9\%$, respectively.Together with an escape fraction of $f_{\rm esc}\approx6\%$, this reduces theavailable budget for hydrogen line emission by nearly half ($f_{\rmH}\approx57\%$). We discuss the impact of the diffuse ionized gas, showing -among other things - that the extraplanar H$\alpha$ emission is powered by LyCphotons escaping the disc. Future applications of this framework tocosmological (zoom-in) simulations will assist in the interpretation ofspectroscopy of high-redshift galaxies with the upcoming James Webb SpaceTelescope.

H-alpha emission in local galaxies: star formation, time variability and the diffuse ionized gas