Complexity of Integer Division
Wikipedia has a nice page about the complexity of mathematical operations, and there is also a dedicated page about division. Asymptotically, division has the same complexity as multiplication. The fastest known algorithm, due to Harvey and van der Hoeven, runs in time $O(n\log n)$. However, this algorithm isn't practical (it is not fast in practice, since the integers aren't large enough). Wikipedia lists no known lower bounds, though some people believe that the complexity should be $\Omega(n\log n)$, and there are some bounds in weak models. See for example Lower Bounds for Multiplication via Network Coding by Afshani, Freksen, Kamma, and Larsen.