The device library displays the installation status for each device in the installed profiles column. When you select devices with installed or pending profiles, you can View profiles in the top bar and the device's right ellipsis menu.
When you view profiles, the Profiles for device dialog opens and you can sort profiles by name, version, state or the date of update, and you can search for specific profiles.
On macOS, the installed profiles appear in the Profiles pane. Click the Apple menu icon and go to System Preferences > Profiles.