Many long time Skype users have been unhappy how the service has changed over the years, especially after the company was acquired by Microsoft. I am one of them.
Starting out as a fairly powerful, secure and private peer-to-peer network, Skype gradually mutated into a client-server product with limited privacy and significantly reduced functionality and performance.
Every now and then I used to make backups of important Skype chats, so I would have the information available for future reference. This used to be doable with copy and paste, but that no longer works. Skype then offered a function to export the chats to a file, for viewing with a viewer.
In late 2017 that chat export functionality was removed from the macOS client in the upgrade from version 7 to version 8. Everything typed in chats after that upgrade no longer gets tracked on the client side but ends up on the server, where of course it is no longer private. According to Microsoft, the chat archives going back as far as April 2017 will be maintained until you delete them.
Skype chat archives after April 2017
To download chat archives, log into your Skype account from a browser using this link:
Skype chat archive until 2017
For older chats, the macOS Skype client has an option to export the locally saved chats. Go to:
Setting / Messaging / Export chat history from Skype 7.x