Terrestrial Warfare
Wars begin when a councilor for the executive faction of one of two rivals selects the War policy against the rival. All war-capable allies of the defending rival (with an army or nuclear weapons) join the war. All war-capable allies of the attacker are given the option to join on the attacker's side.
To win a war, an army must occupy the enemy's capital region. At that moment, the war ends, triggering a regime change event. Claimed regions change hands to the occupier and its allies. If any of the invaded nation remains, its control point owners are replaced with those of the victor. Some of the nation's stats change when a new regime is installed, sometimes in unpredictable ways, but the new ruling faction will be able to fund Direct Investments into the nation without paying an influence cost for a period of one year. Unoccupied regions and surviving enemy armies will contribute to greater unrest following a regime change.
Wars may also end with a simple peace where both sides return to the prewar status quo.
Armies
Armies represent multiple modern divisions that are capable of gaining and holding territory in other nations. Control of an army is gained after councilors gain at least partial control of a nation. Most nations don't have armies at the campaign start, but nations with sufficient population can build new ones with enough investment. While powerful, armies are a drag on a nation's economic development and remain subject to the international relations of their home countries, which too can be managed with sufficient control of a nation.
Armies have a headquarters region in their home nation. If located there, they incur a smaller cost to the nation's economic development.
Armies rely on two key values: its parent nation's miltech level and its strength. The strength value measures how much damage the army has taken. Armies repair themselves when not fighting in a friendly region.
Some armies have a Navy upgrade that allows them to transit oceans. During wartime, a nation's navies can only cross the water if the nation has naval superiority over its foes. Only larger or wealthier nations have the capability to build and project power with navies.
Army Battles
If at least two enemy armies are in the same region, they will fight. Mechanically, each army takes a shot once a day. Its chance of successfully damaging an enemy army is based on its miltech level, strength, whether any councilors are lending their command attribute to the army's nation via the Advise mission, and whether it on defense and the region has the "rugged" flag set.
If an army is in an enemy region and no enemy armies are present, it begins occupying the region, battling the local defense forces (who use the nation's tech level) and taking damage from them. Badly damaged armies will attempt to flee to a safe place without you doing anything, but they can also be destroyed entirely when their strength reaches zero.
If a region is fully occupied it ceases fighting, but it can't change hands until the war is concluded. Regional economies and space facilities can take significant damage during fighting, although the rate of damage goes down as miltech goes up (representing more precise weaponry). Sufficient damage will count as an atrocity by the army's owning faction.
Army Operations
The faction that controls an army can conduct operations with it. They are:
Nuclear Warfare
Some nations have a number of nuclear attacks available to them. These represent launching multiple strategic nuclear weapons at a target region. Launching nuclear strikes will devastate the economy of a region and the enemy armies within it, although the damage will be somewhat mitigated if a nation is launching strikes on its own or an ally's territory. Launching factions will be charged with committing one or more atrocities. Detonating a sufficient number of nuclear weapons may also have disastrous global effects.
Completing the nuclear weapons priority can add more nuclear attacks for a nation.
Nations construct nuclear weapons as a deterrent to enemy invasion. Attempting to conquer a nuclear-armed nation will almost certainly lead to nuclear strikes in retaliation.
Launching nuclear weapons will do terrible and lasting damage to the targeted region, destroy any enemy armies and all space facilities, and surely be seen with horror around the globe.