As soon as you start recording the Skype call, you'll need to let everyone in the call know they're being recorded so there are no surprises.Skype call recording is completely cloud-based so you don't need to worry about your device's performance or storage space as you record. Wish you could record your mom's face when you give her the big news? What about capturing your study group's deep discussions? In Skype you can record your Skype calls directly in the app.