This workshop brought together researchers working in the study of black holes interacting with material sources through long time scales. A focus group of researchers came together to exchange ideas and methodologies for an accurate analysis of such systems. In particular, a Barausse-Lehner have recently developed a Post-Newtonian based formalism that accounts for an improved treatment of black hole effects on matter. As well the group of Enrico Ramirez-Ruis (UC Sanda Cruz, USA) has developed highly sophisticated simulations which account for microphysics. This collaboration aims to combine these two efforts into a unified treatment able to target key astrophysical phenomena