The intracluster light (ICL) is a unique tool to explore the assembly of clusters of galaxies over cosmic time. The ICL is thought to form by the stripping of satellite galaxies as they fall into the cluster. This means the amount of stellar debris floating in the gravitational potential of the cluster informs us about the violence and the timing of the processes that shaped the galaxies making up the cluster. In this talk, I will present the latest advances in our understanding of the ICL. Using the multiwavelength observations provided by the Hubble Frontier Fields, I have analysed the stellar populations of the ICL in 6 clusters at z~0.4, a particularly interesting time to explore the ICL as it is predicted to have formed since z~1. Our results suggest that the ICL of these massive (> 10^15 Msol) clusters is formed by the stripping of MW-like galaxies that have been accreted at z<1, in agreement with current simulations. Furthermore, the slope of the stellar mass density profile at high halo masses resembles the underlying dark matter profile, an indication that the ICL is a more powerful observational tool than previously imagined.