They're pretty well-supported now, I did my blog's entire CSS in vw units.
The only major browser that apparently doesn't support vw is Android stock browser (Chrome on Android does support it). Even my PS Vita browser supports the units.
However, not all CSS styles support viewport units. border-width, a few others. But you can define the doc's font-size in vw (font-size: 1vw;) and then use rem units everywhere to get around those few compatibility issues. (It works.)
