Before I started my last game, I decided to fight with nothing but carriers (if I could put off war for that long). After playing, I've since determined that carriers are really over powered.
How they work:
You research the carrier tech. You design a ship that uses a carrier module. You build the ship. You then send the ship into combat.
Before battle, each carrier module will spawn 5 tiny hulled ships to fight in battle. At this time, they are the tiny hulled laser ships (so you might get 5 sniper M3). I haven't found any way to tell these carriers to use a different kind of ship (such as missiles). These ships are spawned at no cost to you. You don't need to build them or pay for them. If you lose some in battle, it might be a few turns before they are replaced, but they will be replaced (at no cost).
Unfortunately, this had lead to some problems:
In my testing, I've found that they seem to be much more useful than big ships. You get more bang per buck, logistics wise, when using these carrier modules. 5 tiny hulls are equal to 10 logistic points. These fighters are fully equipped for combat. Not only that, but if there is room left over, the carrier ship can carry weapons and other ship parts as well. Further more, you are not limited to just 1 carrier module per ship. You can place as many as you have room to stuff them on. You can design ships with a ridiculous number of fighters. I have with late game research, using ship capacity and carrier miniaturization techs, got the space needed to get 7 carrier modules on 1 huge ship (which amounts to 35 fighters, equivalent to 70 logistics points), and got the spaced needed to put 1 carrier module on a tiny hull (sacrifice 1 ship to get 5 more). This blows logistics way out of the water. 40 logistics points is close to upper limit, but 70 because of 1 ship?
Another observation is that the fighters are quite disposable. If you lose some, they will eventually be replaced (at no cost to you). You don't need to worry about longevity of the fighters. You don't need to worry about being put out of commission for the same duration as a normal ship is after being damaged. I'm not sure how long it takes, but I wouldn't be surprised if it were 5 to 10 turns. A much larger and tougher ship could be out of commission for 50 to 100 turns. Plus if survivability is not a factor, then you can focus on weapons and less on defense (though defense does help). The only defense you need to worry about is to kill the enemy before they can bring harm to the carriers, the fighters are the defense.
Finally, these fighters uses the latest and greatest in technology. They are kept up to date automatically. There is no need to worry about upgrading your ships, or moving them some place safe to upgrade. Their greatest weapon doesn't need upgrading. This means that you could research all the techs you need to design a good carrier ship, and then build them and send them out while you research the weapons needed to design good fighters (which the carrier doesn't need to be good at). In the last war of my game, I was taking out strong ships using my oldest carrier design. I even had a small hull be equipped with 1 carrier module and it successfully killed some large hulls (it had some great fighters).