Proof of Work
What even is Proof fo Work? Proof of Work (or PoW) is a technique where a machine can proof that it used (some) processing power. Even simpler: A way to pay with processing power.
You may ask yourself, what PoW has to do with captchas? That's a good question! Let me explain: The goal of captchas is to make sure that only real humans can do something. Do captchas do their job well? Are they impossible for machines? I mean, we're even having websites which solve captchas for you (~2.95$ per 1000 captchas). So captchas only make it more difficult/expensive for attackers to do something, right? PoW does the same in this situation: The attacker has to pay with processing power to do something. What makes PoW better than captchas, you may ask. I tell you: PoW doesn't annoy the user! They just run in the background and nobody can influence them. You can only speed it up by providing more CPU-power. PoW could also annoy the user, since he could be waiting for the PoW to resolve and couldn't do anything to speed it up.
Conclusion
I am not 100% sure if we should replace captchas with PoW, but in some cases, it makes sense (in my opinion), for example on pages where the user spends some time entering data, eg. sign-up pages.