Eh?
Browsers will sometimes implement their own extensions to various standards (which are sometimes incorporated into those standards), but there is certainly a standard DOM API. If you're referring to older versions of IE, they're the ugly ducking, and the situation has since improved dramatically.
jQuery was a great idea back in the day to avoid compatibility headaches, but with modern DOM APIs and CSS3, the only time I personally use jQuery is if my coworkers decide to use it.
https://developer.mozilla.org/en-US/docs/Web/API/Document_Ob...