Invade
As the name suggests, this military action is focused on aggression and taking over a rivals land whilst they are still inhabiting the region.
Selecting the invade option with a 'Trebuchet' unit present will result in an attempted colonization of the enemy's base.
During this process your army will attempt to destroy any defenses set up by the defending player including armies and towers. If you successfully manage to defeat the defenses of your opponent you must also bring their population down below 500 in order to claim the city as your own.
When the population reaches below 500, you can then send out an army with certain amount of 'Colonizers' to lower the stability of the target city and eventually capture it.
Please note that whilst the invade option involves risk and the loss of personnel, any cities captured via this method will retain their buildings and research levels allowing you to strengthen the city far faster than building from scratch.