The Battle Log shows you who has attacked your land. You will not see the icon until you join an Alliance. It is on your kingdom view screen, and also on your world screen.
The Battle Log shows the players who have attacked you and from the screen below, you can then chose to take revenge on them. These are highlighted in red.
The Revenge button will be there if the player is still located in the same league, so if the player has been promoted you may not be able to find them, so make sure you are quick to revenge.
The Battle Log also show the lands that you own that have been successfully defended by your Titan and Troops as well as the Titan used by your opponent to attack you. These are highlighted in green.