In their book Computer Age Statistical Inference, Brad Efron and Trevor Hastie give a nice description of neutral networks and deep learning.
The knee-jerk response [to neural networks] from statisticians was “What’s the big deal? A neural network is just a nonlinear model, not too different from many other generalizations of linear models.”
While this may be true, neural networks brought a new energy to the field. They could be scaled up and generalized in a variety of ways … And most importantly, they were able to solve problems on a scale far exceeding what the statistics community was used to. This was part computing scale expertise, part liberated thinking and creativity on the part of this computer science community.
After enjoying considerable popularity for a number of years, neural networks were somewhat sidelined by new inventions in the mid 1990’s. … Neural networks were passé. But then they re-emerged with a vengeance after 2010 … the reincarnation now being called deep learning.