I'll discuss some old work of mine on the problem of efficiently computing isomorphisms between finite fields (expressed as quotients of polynomial rings over the prime field). The main result (refining some ideas of Pinch) is a probabilistic algorithm for this problem that for most fields GF(pⁿ) (or all, given some reasonable number-theoretical assumptions) has complexity O(nM(n)), where M(n) is the complexity of multiplication in the field.