Skype is now accessible from email, calendars, and Twitter thanks to the most recent update that Skype has put out for the Skype Extension in Google's Chrome browser. If you don't use Chrome but you do use Skype for work or personal communication purposes, the update to the Skype extension might be a reason to start using Chrome, as it's now possible to create a Skype call link easily and effortlessly from within various tools, whether those be email, calendars, or social media.
At the moment these new links will only work with two different calendar apps and three different email apps, and one social media service. These include Microsoft's Outlook Calendar and Outlook email, as well as Gmail, Google Calendar, and Inbox by Gmail, and the finally on Twitter. For the email compatibility, creating a Skype call link will be accessible from within the "compose email" screen which means you won't be able to create a link to share just from the main screen of these services. This should make sense as it's inside of an email where you will generally be looking to add in a link that shares the Skype call. You should see the new Skype button appear in the compose window whether it's a brand new email or one that you're replying to, so long as you have the Skype extension installed on your computer.
For Google Calendar and Outlook Calendar, the idea is the same, and whenever you go in to create a new item or event inside of your chosen calendar there will be a button to create a Skype call link that you can add to the calendar item before adding people to it. Lastly, for Twitter, whenever you go to create a new tweet, the button should be there next to the button for adding your location. While this could really be used for anyone who sees your tweet and clicks on the link around the time you're doing a call, Skype uses an example of allowing users to create the Skype call link when you're creating an AMA using your Twitter feed as the entry point. If you have the Skype extension installed, the update should already be live.