When you receive Battle Items and Loot in the game, a notification will pop-up (or if you are not in the game, when you login) detailing each item that you have received.
In case you missed the pop-up notification before seeing the items that you have received, you can also check by:
Tapping the Menu icon > Inventory icon
A red square will appear above the Inventory icon which shows a number. This corresponds to the number of new items you have received. All new content in the Inventory, Hero and Troop Roster are highlighted by the glowing 'New' notification.
Please note - if you already had the items received, you will not see the "New" notification above the item.