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In this talk,I will discuss the existence and asymptotic behavior of traveling wave solutions to Allen-Cahn equation with fractional Laplacians where the double well potential has unequal depths.A key ingredient is the estimate of the speed of the traveling wave in terms of the potential,which seems new even for the classical Allen-Cahn equation.I will also discuss nonexistence of traveling wave solutions to a nonlocal combustion model.The talk is based on recent results obtained jointly with Tingting Huan and with Mingfeng Zhao.