It would be great to have the ability to access and add conversations to projects via the app.
Hi @Nicole_phillips1, welcome to the Asana Community Forum!
You can access your messages (previously named conversations) in the iOS app following these steps:
- Type the name of your Team in the search to access the team
- Tap Messages
- Then, tap the Messages icon in the button right corner. See screenshot below:
I hope this helps! 
In iOS app, where can I find messages I received in the past? More specifically, the messages not related to any projects.
I’d like to see received messages in the app, so that I can reply to them on the move.