WhatsApp Web has expanded to Mozilla Firefox, and possibly other browsers too. iPhone and iPad users are still out of luck, as Apple's technical restrictions made it difficult for the Web client to work with iOS version of WhatsApp.
When WhatsApp Web was launched, it was only available for Google Chrome. WhatsApp Web took advantage of Chrome's push notification system, citing it as ideal for the product (ref). However, it is now available on Firefox as well, a browser that still remains popular among many, despite all the recent flak it received.
Many Chrome users had switched back to their old favorite Firefox after Chrome unveiled a new "security update" that essentially destroyed their ability to have custom add-ons - Chrome was now locked to work only with add-ons approved on the Chrome Web Store. A lot of such users will be happy to finally get rid of Chrome altogether, if they had still been running Chrome to use WhatsApp Web.
That being said, I found that WhatsApp Web is quite sluggish on Firefox for Windows, and the animations are very choppy. The scrollbars are the same ugly ones we see everywhere on Windows, and they look out of place. In Chrome, WhatsApp Web runs smoothly, all the animations are slick, and the scrollbars are nice, simple and matching.
Moreover, Chrome has a nice feature called "application shortcuts" which lets me run WhatsApp Web as though it's a desktop app I installed on my computer. Firefox doesn't have a similar feature, and it seems add-ons that were supposed to add the feature are outdated not in active development anymore. (Unfortunately, Chrome for Mac OS X does not have "application shortcuts" native, but fortunately it can be achieved with third-party add-ons.)
So for now, while my main browser is to remain Firefox (I too deserted Chrome after their security lockdown), I will continue to use Chrome for WhatsApp Web. What about you?
PS: There are some negative comments about WhatsApp, telling that it's better to switch to competitor X or Y. The problem with this suggestion is that, while easy to say, it's hard to do. When all of your friends are on WhatsApp, you will find that you cannot switch to another chat client expect everyone to follow. I find that even though I have accounts on many chat clients -- like Telegram, WeChat, Hangouts and even Facebook Messenger -- ultimately I only use WhatsApp on a daily basis (to be honest, I like Telegram better).