Classical Island Biogeography Theory as founded by MacArthur and Wilson in the 1960s considers island biodiversity as the result of a dynamic equilibrium between colonization and extinction. However, this theory is missing two essential ingredients: 1) particularly for remote islands, there is an additional source of diversity:speciation 2) biodiversity on many islands is not in dynamic equilibrium. In this talk I will present a new Island Biogeography Theory that we have been developing in the last 6 years: DAISIE. DAISIE stands for Dynamics of Island Biota through Speciation, Immigration and Extinction and can be used to simulate various scenarios of island biogeography and make inferences on the basic processes of Colonization, Extinction and Speciation. I will some of the details of this framework and some of its applications.