Click “Save As” to download it to a location of your choice on your computer. In Skype for desktop, hover over the video in the chat and then click the “More options” menu button to the right of the thumbnail. While the recording is only available on Skype’s servers for 30 days, you can download it and keep it for as long as you want. Skype downloads recordings as MP4 files. The recording is only available for 30 days and is removed from Skype’s servers after that. It appears in your Skype chat after finishing the call, and everyone on the call can view, save, or share it. Your call recording happens “in the cloud” and is stored on Skype’s servers.
Other people on the call will see a banner saying that you, specifically, are recording the call. Other states are “two-party consent” states, which means everyone on the call needs to know it’s being recorded. Some US states are “one-party consent” states, which means only one person on the call (you) has to know the recording is happening.