You can use SVGKit for example.
1) Integrate it according to instructions. Drag&dropping the .framework file is fast and easy.
2) Make sure you have an Objective-C to Swift bridge file bridging-header.h with import code in it:
#import <SVGKit/SVGKit.h>
#import <SVGKit/SVGKImage.h>
3) Use the framework like this, assuming that dataFromInternet is NSData, previously downloaded from network:
let anSVGImage: SVGKImage = SVGKImage(data: dataFromInternet)
myIUImageView.image = anSVGImage.UIImage
The framework also allows to init an SVGKImage from other different sources, for example it can download image for you when you provide it with URL. But in my case it was crashing in case of unreachable url, so it turned out to be better to manage networking by myself. More info on it here.