The gradual Skypification of all things Microsoft continues this week, with Skype for Web picking up the ability to call both landlines and mobile phones, plus a few other new features.

“Last year we brought you a web version of Skype which lets you get straight to your Skype conversations from any computer,” a new post to the Skype Garage & Updates blog notes. “Skype for Web is great whether you’re using a shared computer that doesn’t have Skype downloaded, or you just prefer using a web version instead of a downloaded app.”

Here’s what’s new with Skype for Web.

Call landlines and mobile phones. Using your Skype credit, you can now call landlines and mobile phones from Skype for Web, just as you can using the desktop Windows client.

Watch YouTube videos without leaving Skype. Thanks to that URL preview feature that’s popping up in Skype clients everywhere, you can now watch YouTube videos directly in a Skype for Web.

Add non-Skype users to a Skype conversation. Already available in the desktop Skype application, you can now add people to a Skype conversation, including people who are not Skype users: Just generate a URL and send it to someone you want in on the conversation.

Notifications. Given the history here, this one makes me a bit nervous, but Microsoft has enabled notifications in Skype for Web. “As long as you’re signed into Skype for Web, you’ll receive notifications, even if you’re in another browser tab or another app,” Microsoft says. Hopefully there’s a way to turn that off too.

You can try Skype for Web now at web.skype.com.