Capturing IMF variations in observations and simulations - how far along are we?

For any given population of stars, the initial mass function lies at the heart of converting mass into light and vice versa. For example, observers use the IMF to derive physical properties from the observed light of galaxies. On the other hand, hydrodynamical, cosmological simulations require an IMF shape for their sub-grid physics, which ultimately dictates the stellar mass of simulated galaxy. However, galaxies in a LCDM cosmology undergo a multifaceted assembly process, which not only emerges due to the complexity of the baryonic cycle, but also their individual merger history. To fully understand galaxy formation, we need to take into account all these complexities from hierarchical assembly, to bursty star formation histories and chemical evolution of individual elements until the variability of the IMF. I will talk about the state-of-the-art of tools that begin to allow us to capture these complexities and how they shape and alter our view of galaxy formation. In particular, I will focus on newest results of the IMF variation in the connection with the abundance of alpha-elements.