Recovering the star formation history of galaxies through spectral fitting: Current challenges

With the exception of some nearby galaxies, we cannot resolve stars individually. To recover the galaxies star formation history (SFH), the challenge is to extract information from their integrated spectrum. A widely used tool is the full spectral fitting technique. This consists of combining simple stellar populations (SSPs) of different ages and metallicities to match the integrated spectrum. This technique works well for optical spectra, for metallicities near solar and chemical histories not much different from our Galaxy. For everything else there is room for improvement. With telescopes being able to explore further and further away, and beyond the optical, the improvement of this type of tool is crucial. SSPs use as ingredients isochrones, an initial mass function, and a library of stellar spectra. My focus are the stellar libraries, key ingredient for SSPs. Here I talk about the latest developments of stellar libraries, how they influence the SSPs and how to improve them.