In 1995, Russell Impagliazzo proposed five complexity worlds:
1- Algorithmica: $P=NP$ with all the amazing consequences.
2- Heuristica: $NP$-complete problems are hard in the worst-case ($P \ne NP$) but are efficiently solvable in the average-case.
3- Pessiland: There exist average-case $NP$-complete problems but one-way functions do not exist. This implies that we can not generate hard instances of $NP$-complete problem with known solution.
4- Minicrypt: One-way functions exist but public-key cryptographic systems are impossible
5- Cryptomania: Public-key cryptographic systems exist and secure communication is possible.
Which world is favored by the recent advances in computational complexity? What is the best evidence for the choice?
Russell Impagliazzo, A Personal View of Average-Case Complexity , 1995
Impagliazzo's Five Worlds, The Computational Complexity blog