The Alliance Battles menu will display all current battles that members of your alliance are engaging in. You can see the participants on both the attacking and defending side. If you decide you wish to join in the battle to help your teammates attack or defend, you can easily do so, by tapping the reinforce button. Information may be hidden depending on your scouting level or who is the attacker/defender for that specific battle.
There is also a Battle History, where you can see all previous battles that have been fought and their outcome while you were away.