There is a long list actually…..
Cross Browser: Start with the links below (all HTML/CSS can be search a w3schools if you need to see if a browser supports a particular tag/CSS attribute…. browse through it a moment and you’ll see why IE is the devil….
https://coding.smashingmagazine.com/2010/06/07/the-principles-of-cross-browser-css-coding/
https://www.1stwebdesigner.com/design/tools-browser-compatibility-check/
Also, pay especial attention to mobile responsive design.
https://www.copyblogger.com/mobile-responsive-design-101/
https://www.sitepoint.com/understanding-responsive-web-design-cross-browser-compatibility/
https://alistapart.com/article/organizing-mobile
The short answer to your question: links should work just fine unless you add some really esoteric html tag and start rewinding to very old IE versions. But how things are displayed can change very significantly. It’s more likely images will look bad, or formats will get wonky, or effects that look cool here won’t look cool there, or the dimensions will go to hell, etc.