The combat system is actually very simple. When a battle starts, the main character's unit is by itself. The first thing the player has to do is summon the other allied units into the battlefield. Summoning units cost the player a certain amount of money, which figures into the game's system of unit upkeep, though it never has been a problem since I have always had enough money to summon all of my units. However, the summoning system does have some difficulties associated with it. The first problem is that summoning units require space. For example, a 2x3 unit requires a 2x3 spot of unobstructed space on the battle grid to summon the unit. Early in the game this is no problem, but later in the game, when the player has seven or so 3x3 units, finding the space to summon every unit becomes a real problem, albeit not an insurmountable one. However, the real problem with the whole summoning system comes as a consequence of other aspects of the combat system.
Combat itself, like in the Ogre Battle series, is very simple. When you attack the enemy, the soldiers in your unit automatically attack the enemy unit using attacks determined by the row they are standing in. Melee attacks are usually executed from the front row, while the best ranged attacks are launched from the middle or back rows. Attacks can hit anything from only a single target on the enemies front row to the entire enemy unit. After your attack concludes, the enemy will counter attack once, if possible. However, there are quite a few complicating factors of this system:
1) Targeting is completely random (or at least determined by unreliable hidden factors).
There is no way to control which enemies each individual character attacks. Even if you want your Archers to shoot the row of enemy Pyromages, they might shoot the row of enemy Knights instead, and there is no way of predicting that outcome. This is much more frustrating in the case of allied support characters, who buff or heal at random. A certain degree of dependability is necessary in games where you have no direct control of the characters.
2) Targeting is done in one big wave.
Even if your first soldier's attack kills an enemy soldier, the rest of your unit can still waste their attacks on that dead enemy. This is particularly troublesome for melee units, which can only target the frontmost row of the enemy, making them generally weaker than ranged units. When this fact is combined with the fact that targeting is random, it means that the effectiveness of attacks can vary heavily.
3) Attacks are often very lethal.
It is often possible to wipe out an entire row of enemies, or lose an entire row of allies, in a single exchange. While melee units are pretty durable with support, mages, archers, and support characters are as fragile as glass, and die quickly to even regular attacks.
4) Once a unit's leader is dead, the entire unit disappears once both sides have attacked.
In a unit lead by a fragile character such as a mage, this means that an entire unit can be lost to a single attack by a ranged attacker.
5) Once a unit has lost even a few key units, its combat effectiveness drops quickly.
Many units are built on synergy. A mage unit with 4 mages in it has more destructive power and access to more tactics and special skills than a mage unit with just the leader. And a melee unit is in trouble if it loses its healer.
On top of all of this, there are also special attack skills that can be used by an attacking unit that has lost 20% of its stamina (the main unit resource besides individual soldier's hit points, which is drained after every action). While these skills vary in their effect (some hit only the enemy leader, while others can hit various rows or columns of enemies, or even the entire enemy unit), any skill will generally kill whatever it hits, particularly if the enemy has taken damage. Since it is really easy to target the enemy leader with one of these skills, since each unit probably has several choices by fairly late in the game, a single use of these skills will destroy an enemy unit. There has not been one battle in the game where I have had to deplete close to a third of uses of these skills in order to win, either. On the other hand, every enemy in the game also can use these skills, so if you let an enemy live too long, it will generally wipe out one of your own units.
Because of all of this lethality built into the system, actions are a very valuable resource in the game. Being able to get the drop on a potentially deadly enemy, such as a large mage group, is essential. This means that ACT is the single most important stat in the game. ACT determines both how often a unit's turn comes up, as well as how far it can move. Units with high ACT will be able to act much more quickly than other units, and move further with each individual movement. In other words, high ACT units will be able to rush in first, wipe out the first enemies, and move on before lower ACT units even have a chance of getting into position to help.
This is where the summoning system can become a problem. When a unit is summoned, there is typically a delay before they can take their first turn. This means that the enemy has the chance to move first. This leads to two different possible starting situations in a stage. In the first, the army has to run a certain large distance to reach the enemy. In this case, your units will have plenty of chances to buff themselves up and wear down their stamina to the point where they can use special attacks, and thus will wipe the floor with the enemy when they arrive. However, the slower moving units will probably be dropped and miss most of the fight. In the other situation, the player starts right next to the enemy. In this case, the enemy will get to move first, and might do some serious damage to the player's units before the player can act.
While every unit possesses special skills called Tactics (usally self-buffs), they don't see much use. The only really valuable buffs are ACT boosting ones, which I often use on the first turn so I can close in on the enemy. However, as soon as my units close in to combat range, tactics become useless, thanks to the value of each individual action. Sometimes I wonder if it would have been better to have made them more similar to swift actions in D&D: actions that don't waste a regular action, but can only be done once a round. The only exceptions to this trend are the mage tactics, which include spells that can hit every soldier in three adjacent unit for enough damage to kill every soldier but the leaders. Those spells are so over-powered that they can make mages really annoying opponents.
One last note; there are two kinds of battle you can fight in the game. These are story battles and Inspections. Story battles are the finite in number battles that progress the game's plot, while Inspections are the randomly generated fights you can try at any time. Unfortunately, Inspections tend to be filled with a large number of enemies that all share a predictable power level, and one leader who is usually way higher in level than the party. For example, my level 24-31 party dove into an Inspection with a listed level of 19+. The boss was over level 70. Even characters that were effective against the boss couldn't land a single hit. Thus, Inspections have so far been very frustrating and difficult. Thankfully story battles have provided plenty of rewards to keep me going through the game.