Since November 2014, Microsoft has been working to build a plugin-free version of Skype that will run in the browser. That work took a step forward today, with support for no-plugin voice and video calling in Microsoft's Edge browser.
However, the support is quite limited. It requires the latest version of Edge, as shipped in Windows 10 version 1511 (build 10586). Both one-to-one and group chats are available in Edge-to-Edge calls without plugins, and one-to-one calls to the very latest version of Skype for Windows and OS X are also plugin-free. But any other combination—different browsers, older versions of Skype, or group calls to the desktop Skype clients—will still need a plugin.