Does spyware for iPhone exist?

I heard in the news that one criminal had put spyware onto his wife's phone, it wasn't an iPhone, but he still could access her texts and could turn on the microphone when they got done with a call. Is it possible for someone to do this to an iPhone? Would there be any signs that your iPhone has spyware?

Absolutely possible to have spyware on almost any device with an OS these days. IOS tablets/phones/computers, Android, windows, linux, etc.

Signs of spyware? Really kind of depends on what the spyware is. Could make your iphone run slower, things are running in the background. But sometimes you can't see signs of anything on your devices. Infections of any kind, try to hide and not be too noticeable.

Best thing to do is invest in antispyware software for your devices.

It is certainly possible. Phones are essentially computers and there can be viruses and malware written for them. Its not too common on iOS since Apple is generally pretty good with security. Any apps that do contain malware are generally very quickly removed from the App store if they somehow managed to make it through Apple's testing.

However, a lot of free and popular apps behave in malware-like ways. A lot of apps try to ask for your location, microphone, camera, etc even when there really is no reason that they need them.

Possible yes
Likely to be on YOUR phone, no.