When you receive Heroes, Troops and Loot in the game, a notification will pop up - or if you are not in the game at the time it will pop-up when you log in - detailing each item that you have received. 

Please note - if you are in the middle of a battle or on the map, you will not see the pop-up until you come back to base.

In case you missed the pop-up notification before seeing the items that you have received, you can also check by:

The same thing is applied to Heroes and Troops. You can check that the new Heroes have been added to your Roster by:

You can check that the new Troops have been added to your Barracks by:

You can also check your Recent Activity Log.