In this talk, I will introduce some new work of ours about the spreading speeds of nonlocal KPP equations. First, we develop the theory of generalized principal eigenvalues and the approach of homogenization of nonlocal diffusion equations. Then applying these new methods, we give some estimates of the spreading speeds of nonlocal KPP equations. Last, we show that the unique spreading speed exists provided the media is almost periodic and the diffusion is irreducible in the sense of probability.

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