The enemy started using their latest flavor of bullshit: massive fighter swarms. My mostly outdated fleets can handle a few dozen, but they were using hundreds at a time. Worse, they had guns that outranged my defense lasers. They didn't outrange main guns, just the lasers, but the main guns have low accuracy against fighters. In fact, their fighters' guns were the same technology as my main guns, just fighter-sized.
My first attempt at repelling them was a dismal disappointing failure that cost me several worlds and many more ships(and a save-scum to undo it). Largely because what I tried were IR lasers, which have massive range, but poor fire rate. And I only put two of those on a single ship; they may as well not have had any. Probably could have used missiles, except the enemy fighters did have missile traps.
Second attempt was simply fighters of my own. Fighters with superior engines, shields, and a pair of IR lasers which aren't as bad on fighters. I was able to put three corvette-sized carriers, carrying 10 fighters each, into battle against two enemy carriers with about 200 fighters total over one of my planets that was under siege. Long story short, in part due to really bad unit AI programming, I was whittled down to 4 fighters against 30 enemy fighters. Using hit-and-run tactics, eventually destroying all of them, and suiciding the rest of my fighters against the carriers. The post-battle screen showed they still had several more fighters they didn't deploy for some reason, but enough damage was done that two of my older frigates could mop up.
With the way clear, I was able to reinforce my troops, and when the enemy attacked again, it was one crippled
* carrier and its fighter compliment against 200 of my superior fighters that I brought in via freighter(you have to "disassemble" them to ship, then assemble at their destination). All enemy forces destroyed in seconds, no losses. Booyah.
Polaris Sector. Now, if only I could figure out how they have spy ships so deep in my territory, far from any fuel source. There is a module that passively regenerates fuel at a star, but I don't think it'd fit on a freighter alongside the cloak, scout, and sabotage modules. I haven't tried myself.