The following browsers are supported when swup is loaded from a CDN.
Transpiling your code with tools like Babel will increase browser support.
Including polyfills for modern browser APIs using a service like polyfill.io will significantly increase browser support. Since it's a moving target that depends on the browsers of your visitors, you're encouraged to do some research of your own here.
If you absolutely need to support older browsers like IE 11, downgrading to swup v3 will get you much closer to that goal, at the sacrifice of some of the newer features introduced in v4.
This support matrix is valid for swup itself — plugins may differ in the list of supported browsers.