If you're using the Steam client, all recent chats will propagate in the chat tab that displays.

On mobile, all recent chats show up.

http://gtm.you1.cn/chat

The steamcommunity url isn't helpful at all (literally just links to the chat page), but as it turns out Fenrir's answer seems to work for mobile, at least for most recent.

If you want to see some chats you closed beyond the window of what's deemed "recent" on mobile, here is a way: https://gtm.you1.cn/helpsteam/en/accountdata/GetFriendMessagesLog

source: https://www.partitionwizard.com/partitionmanager/steam-chat-history.html

This thread was quite old before the recent post, so we're locking it to prevent confusion.