Neural nets have been around for a long time. Why are they popular only now?

Neural nets have been around for quite some time. They have become popular only in the last few years. How come?

Here are two slides from Geoffrey Hinton's talk summarizing the problems:
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Geoffrey Hinton quickly addresses the question in his 'talk':https://www.youtube.com/watch?v=IcOMKXAw5VA&feature=youtu.be&t=21m29s
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I recommend the whole talk
https://www.youtube.com/watch?v=IcOMKXAw5VA&feature=youtu.be&t=21m29s

Watch the entire talk!
 

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