It’s been around for years, and has the highest range of player skill of any mahjong client from beginner up to really heavyweight pros. It doesn’t have frills, bells, whistles, distractions, or dubious imagery.
The original interface was all in Japanese. Some people – including me – have worked with the developer on its localisation. Some of that work is now built into the website, but there is still a lot of untranslated japanese text in it.
So there are browser add-ons to make it easy to use for people who don’t read Japanese.
Tenhou is free to use until one reaches the very top levels. (That’s for the /3 interface. For the fancier interface, only the beginners’ room is free)
You can use the site without the browser extension, and you’ll get some text in English and some in Japanese. For some people that’s ok; for others – including me – that was insufficient to be able to use the client.
There are several plugins available to improve your experience. Click on the screenshots to enlarge them.