Are there risks of jailbreaking my iphone?

I want to jailbreak my iphone, just for some of the themes I can add and for some other small stuff. I was wondering if there are risk of doing so or if I could damage my phone in any way?

There are some minimal risks, but if you use popular jailbreaking methods on right model of iPhone, risks are negligibly minimal.
The logic is fairly simple, the more people do it, the more problem are discovered and fixed, as a result, older iPhones can be very reliably jailbroken. For very new models when they just hit the market there might not be a good way to do that.

On the technical side, jailbreaking is just a software update, so you can't technically damage the phone, the real risk is that if jailbreaking WILL go wrong it might be hard to undo it and restore original iOS, so make sure your computer will not turn off or some kid won't yank the USB cable in the process, and don't run anything else that might affect computer performance while doing the jailbreaking.

Here's one good article about iPhone jailbreaking: http://www.gizmag.com/jailbreak-guide-iphone-5-ipad-4-ipad-mini-untethered-ios-6-1/25995/ Use it on your own risk.