In the battle page, you can find a list of opponents that you can either invade or duel. The list will show each person's name, battle rank, demi alignment & army size.
Each time you win against an opponent, you will gain battle points, experience, gold and demi points (up to 10 per day each). If you lose against an opponent, you will lose battle points, gold and health. There is also the chance than you can eliminate an enemy if he/she is close to dying, and vice-versa. Each time you win or lose a battle, the battle counter on your Keep page will increase. Eliminations have its own separate counter.
The battle points you earn are used to climb the battle rank. Beating someone with a higher battle rank will reward you with more battle points, while beating someone with a higher level will reward you with more XP. Attack and defense stats are the most vital factor when battling, along with army size and equipment. When battling, your best equipment is automatically chosen by the game, and used against your opponent.
When invading, your army size comes into play. You can take up to 501 army members into an invasion. Each army member can bring 1 unit, 1 item and 1 spell. Additionally, for every 5 army members that go into an invasion, 1 general also joins in (up to a maximum of 101 generals).
The outcome of an invasion is determined by stats of generals, units, items & spells, and by personal stats. There may also be a luck factor involved if you and your opponent are evenly matched.
Dueling is a one-on-one match between the generals of you and your opponent. Hence, your army size does not come into play when dueling. Each general takes the best item of all your weapons, off-hands, helmets, armor, amulets, spells and gloves into the battle (for more info about the best items, see the Best-in-Game Armor Set.
The outcome of a duel is determined by stats of generals, items, spells, and by personal stats. There may also be a luck factor involved if you and your opponent are evenly matched.