I’m not sure I’d say NN was the first major breakthrough.
For many years people considered them too inefficient to compete with SVM, and people genuinely thought kernels was the way to intelligent machines.
Today you find researchers claiming that Bayesian nets will outcompete NN.
We’ve also seen tremendous success of random forests and other ensemble models.
I am sure there are plenty of researchers looking into all sorts of novel ensembles.
I think the major breakthrough is ensemble models and with a little bit of cheekiness you can say that NN are ensemble logistic regressions.