As of now, you can install a PWA version on desktop and mobile. Included some instructions below on how to do this for each platform. Make sure you are browsing the main site while performing these steps, as the forums have a separate PWA app.
Functionally, the PWA isn't much different from a potential native app and we can do things like push notifications through it (currently not setup at the moment). However, we're still also working on a version that will be published to Apple and Google Play app stores. This is what the PWA looks like on my desktop and it gets its own icon in the dock as well:
Mobile - iPhone/iPad
In Safari, click the Share icon and select "Add to Home Screen" in the menu that pops up. Then select Add. This will add an icon for the app to your home screen that you can just tap on rather than going through Safari.
Desktop - Chrome
In Chrome on a desktop, click the "Install" icon next to the star in the website address bar. It will show a popup as depicted below. Click "Install" to add the app to your desktop. From here, you can use the OS controls to pin the app to taskbar if you desire.
Mobile - Android/Chrome
In Chrome, click the three dots at the top right, then select "Add to Home Screen". Click Add in the following prompts and then you should see the Exophase app added to your home screen.