Currently, there are two ways that you can integrate tribe with your mobile app.
Everything in tribe is available through tribe REST API. One way of implementing tribe natively in your phone app is to use tribe's API and implement the interface which best suits your app.
Although this method gives you total freedom and the most flexibility, it can be hard to implement.
Web View Integration
A very common way of integrating tribe with mobile apps is through Web View integration. In this method you'll be embedding a web view inside your mobile app. The web view endpoint is customizable and can include or exclude header and have custom CSS.
In this method, you can use JSON Web Tokens (JWT) to implement the Single Sign-on. This means that your app will generate an encrypted token with user's information using a secret key available in Admin panel. Your app will pass the JWT using query strings and tribe will login the user based on the encrypted information.
This method is the more popular and easier way of integrating tribe with your phone app.
It's also worth mentioning that custom tribe apps and web hooks make it possible to send in-app push notifications when a new action happens in tribe.