 First, we have a better understanding of the applicability of mathematics to the world. Indeed, understanding the ‘unreasonable effectiveness’ of mathematics in discovering and accounting for the laws of the physical world (Wigner 1967, Steiner 1998 and 2005, Pincock 2012, Bangu 2012) can only be resolved if we understand how mathematics helps in scientific explanation. Second, the study of mathematical explanations of scientific facts is extensively being used as a test for theories of scientific explanation, in particular those that assume that explanation in natural science is causal explanation. Third, while the debate is still at a standstill, philosophical benefits have also emerged in the metaphysical arena by improved exploitation of various forms of the indispensability argument. Whether any such argument is going to be successful remains to be seen but the discussion is yielding philosophical benefits in forcing, for instance, the nominalist to take a stand on how he can account for the explanatoriness of mathematics in the empirical sciences. In addition, mathematical explanation plays a role in theorizing about mathematical coincidences (Lange 2010b, Baker 2009c), an interesting area of metaphysical investigation that had already been developed in the context of causal phenomena (see Owens 1992). One should also expect future developments emerging from the interaction of the analysis of grounding and mathematical explanation.  