Elephant mtDNA and nuclear DNA phylogeny from Meyer et al. 2017. The Neumark-Nord (NN) and Weimar-Ehringsdorf (WE) straight-tusked elephants are indicated. The mtDNA tree has a time scale (bottom) but the nuclear DNA tree has no time scale associated with it.
John Hawks has a lengthy and fact filled post about our improved understanding of the evolution of the elephant (most species and clades of which are extinct now), which has been enhanced recently by ancient DNA and new paleological finds. Some important parts of this evolution happened while modern humans existed.