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The gravitational-wave observation GW150914 by Advanced LIGO provides the first opportunity to learn about theoretical physics mechanisms that may be present in the extreme gravity environment of coalescing binary black holes. The LIGO collaboration verified that this observation is consistent with Einstein's theory of General Relativity, constraining the presence of parametric anomalies in the signal. In this talk, I will discuss the plethora of additional inferences about gravity that can be drawn from the absence of such anomalies in the LIGO observation. I will focus and classify these inferences into those that inform us about the generation of gravitational waves (e.g. the activation of scalar fields, black hole graviton leakage into extra dimensions, the variability of Newton's constant, the breakage of Lorentz invariance and parity invariance), and the propagation of gravitational waves (e.g. the speed of gravity and the existence of large extra dimensions). I will conclude with a discussion of how these inferences may inform us about the models of modified gravity in cosmology.