Don't look at gevent for Python, look at a responsible async library: asyncio if you like Py3, Twisted if you like Py2 and want something that's very featureful but old-school, Trollius if you wish you could be using asyncio but you're stuck on Py2.
gevent is too much magic. It aims to give you async without changing any of your code. To accomplish this, it monkey-patches the entire Python standard library, in a way that is 99% compatible with Python, but the 1% will constantly surprise and infuriate you. Its compatibility shows no signs of increasing given how much its development has slowed down.
You can use gevent as a quick hack, but you will hate yourself if you have to maintain gevent code.
You make a valid point, but many years of work have gone into the monkeypatching at this point. If you use the latest version, it's very rare to find a place where it fails. It's usually only an issue if you're dealing with a third party module that makes use of native shared libraries.
I use gevent both for small and large projects, and haven't had any complaints. The monkeypatching pains my soul just a little bit, but I've found no better async framework for Python yet.
gevent is too much magic. It aims to give you async without changing any of your code. To accomplish this, it monkey-patches the entire Python standard library, in a way that is 99% compatible with Python, but the 1% will constantly surprise and infuriate you. Its compatibility shows no signs of increasing given how much its development has slowed down.
You can use gevent as a quick hack, but you will hate yourself if you have to maintain gevent code.