Current integral field spectrographs like the MUSE instrument at the Very Large Telescope provide a wealth of high quality hyperspectral data for nearby galaxies. These spectra contain information about the kinematics, ages and element abundance ("metallicity") of the stellar population inside the galaxy, which in return provide us with a fossil record about how the galaxy assembled its stellar mass. Characterizing a galaxies stellar population in terms of their ags and metallicities allows us to characterize, whether its stars were formed within the galaxy itself, through the conversion from gas to stars ("in-situ"), or were accreted from mergers with other galaxies ("ex-situ"). For example, lower mass galaxies are less efficient in forming stars, hence their stellar populations have lower element abundances. Thus, if such a galaxy is then accreted by a higher mass galaxy, their stars spatially mix, but their origin is still distinguishable in the age-metallicity space. However, reconstructing the ages and metallicities of stellar populations from integrated spectra is a highly ill-posed and ill-conditioned inverse problem. I will talk about results from the state-of-the-art method of reconstructing a galaxy's merger history that uses optimized regularization techniques and was validated on numerical simulations of galaxies (https://ui.adsabs.harvard.edu/abs/2020MNRAS.491..823B/abstract). I will further discuss scientific limitations and technical difficulties we are currently facing to apply this method reliably to observations and provide an outlook to future developments.