The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as $1/r^alpha$ at distance $r$? Here, we present a definitive answer to this question for all exponents $alpha>2d$ and all spatial dimensions $d$. Schematically, information takes time at least $r^{min{1, alpha-2d}}$ to propagate a distance~$r$. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.
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