Where can I find information on what was happening on my base when I was away?

The Events menu (curtain menu on the left) displays the last 50 attacks on the player’s Base and Resource Centers.

The Replay button allows a player to watch enemies' attacks on the Base or Resource Centers, regardless of whether it was successful or not.

Revenge becomes available when the enemy successfully attacks a player’s Base. As a part of a revenge attack, the player can scout or attack an enemy's Base. Regardless of whether the revenge is successful or not, there's no second attempt. Neither can you take revenge on someone who has taken revenge on you.