And how do the constraints differ in practice on various browsers?
The w3c makes no mention of size limits meta at w3c.org. As for browser implementations, you would need to look at the individual browser's source code and/or documentation.
I think the general view is that if you think the length of your META tag might be too long, then it IS too long!
For keywords and description tags I realized some folks want to stuff every possible term they can think of in there but its a lost cause. The content of your site will get you ranked in Google and similar much better than spamming the META tags.
How Google uses Meta tags which describes using a short description... and Google doesn't even look at the "keywords" tag. (which is typically the one SEO trigger happy marketing folks stuff full of crud)
Meta Description Tag Length: It’s not the number of words that count. It’s actually the number of characters length. Because, Google will cut off anything more than 155(roughly) characters. Optimizing for in the description and try to limit its length to 25-30 words. Also try to use no more than two sentences.
Taken from http://online-seo-information.blogspot.com/2009/01/meta-description-tag-length-examples.html