We will discuss a new algorithm for computing geodesics in the curve complex. This uses a refinement of the ideas of Masur-Minsky, Leasure, Shackleton, Watanabe and Webb to ensure such geodesics are found in polynomial time (in terms of their length). One corollary of this is a new (polynomial-time) algorithm to determine the Nielsen--Thurston type of a mapping class. This is joint work with Richard Webb.