Deep observational studies reveal that galaxies are surrounded by a faint, diffuse stellar component: the intra-halo light (IHL). The IHL is typically referred to as the stellar halo in galaxies and the intra-cluster light in galaxy clusters. Regardless of mass scale, the IHL is believed to form primarily from the remnants of accreted galaxies, providing a valuable probe into a galaxy's assembly history. In this talk, we explore the formation of the IHL using a sample of galaxies drawn from the EAGLE suite of hydrodynamical simulations. First, we introduce the dynamical decomposition technique used to isolate the discs, bulges, and IHL of galaxies whose masses range from that of the Milky Way up to that of massive galaxy clusters. After characterising the present-day properties of the IHL for these galaxies, we study the formation and assembly histories of their in situ and ex situ components. Although the IHL of most galaxies is dominated by ex situ stellar mass, a significant in situ contribution also exists, with the formation mechanisms of the in situ IHL varying depending on the host halo mass. To conclude, we examine the role of mergers in shaping the present-day IHL of Milky Way-mass galaxies. Specifically, we show that while many Milky Way-mass disc galaxies with low-mass IHL exhibit quiescent merger histories, others have experienced significant mergers since z=1. We discuss the origin of this result and potential implications for studies aiming to reconstruct the assembly histories of galaxies from observations of their IHL content alone.