At now most of popular messages (Telegram, Facebook, Viber, WhatsApp, etc) have ability to store chat logs on server and retrieve history from server, sync history between devices. Opensource XMPP IM servers Ejabberd and Prosody already have build-in support for XEP-0313 Message Archive Management, so this is easy to enable now on any XMPP server. Please add ability to retrieve and sync chat log message from archive on server in next versions of KDE Telepathy, this is very useful feature. Some other Jabber clients already impement this feature, for example Gajim - maybe we can re-use code from this project?
Here is list of projects that already impement MAM support: https://www.zash.se/mam.html
Additionally to XEP-0313: Message Archive Management I would also include: XEP-0280: Message Carbons to send copies of both your sent and received messages to all devices.
Dear user, unfortunately Telepathy is no longer maintained. Please migrate to another solution, e.g. for Jabber a possibility is Kaidan, for Matrix a candidate is NeoChat.