Cross-browser compatibility can be a major pain. The philosophy for most web developers is to code against a standard-complaint browser (Chrome), then apply CSS hacks later for other browsers that need to play catch up (Internet Explorer). In other words, it is better to make your code forward-compatible and apply backward-compatible hacks instead of the other way around.
One technique for cross-browser compatibility is using conditional comments in the HTML like this:
This works great, but it is very awkward and ...