I enjoyed it. I'm hoping for a Season 2. It's a mecha show and so I'd have normally avoided it, but it's also a good one with relatively few mecha battles and much more screen time given to its characters.
Story outline! YUKINA SHIRAHANE is an ordinary teenage girl whose high-powered mother is the director of Kurobe U.N. Research Institute. KENNOSUKE TOKISADA OUMA is a teenage samurai from 450 years ago who's been bonded to a giant war robot. Unfortunately he's going to need Yukina as his co-pilot, because it won't work otherwise. No one understands that one for a while. Meanwhile the EFY DOLGH are aliens who don't like us and have lots of giant war robots.
I think that's all you need, really.
What's good about the show is that it's not about fighting the Efy Dolgh, who don't actually attack us that often. They're up there in space. They're bad news. However our heroes aren't living in a warzone and this isn't a war series. On the contrary, everyone goes to school as usual and the show's going to some pains to spend time on school festivals, terrible summer holidays and goofy home-made movies with everyone dressed up as a zombie or a hopping vampire. They'll do this even when the world seems to be ending. This is important. They don't believe in gloom and doom. The U.N. recruit Yukina and Kennosuke as mecha pilots, but they're also a bit dodgy and also employ dissection-happy doctors and foul-mouthed idiot mecha pilots. (His name's Tom. Other U.N. fighters include a podgy but super-competent butler, a nearly mute Chinese girl and a French girl called Sophie who wishes she was a samurai.)
This cast is the show's chief focus, by miles. They're funny. Kennosuke vs. the 21st century is a laugh and the show builds some likeable, fresh jokes about him. (His frozen face in class in ep.12, for instance.) Yukina's best friend Mika is a joy to be around. There's character development, with the obviously doomed crush of Ryoto being taken more seriously than I'd expected and eventually leading to character growth. There are darker elements in people's backstories. Yukina's father disappeared years ago and everyone laughed at her because he was a famous nutcase. Meanwhile the balance between the show's character-based elements and its more action-based mecha storyline is well done, somehow managing to feel realistic even though schoolchildren are defending the Earth. Parents might decide to leave town, or even the country, while the U.N. will get a lot less friendly if it's getting official requests about you from abroad.
The space stuff works well. The Efy Dolgh are swaggering cocks who don't call for back-up if they get in trouble because they don't want to share the glory. They're a bit like empire-building evil samurai, which is a nice counterweight to the show's overall reverence for samurai and traditional stuff. When Kennosuke gets a careers advice chat in ep.24, the teacher seems to see "samurai" as an ideal and a set of ethical principles rather than, say, a social class of thugs that was abolished in the 19th century. (Mind you, there's a bit in ep.24 where Kennosuke demands "Why do we have to be so obsessed with reputation?")
I don't even mind the giant robot battles. Mecha fight scenes are fundamentally dull and my interest would wane during the more battle-heavy episodes like ep.6, but the show isn't going overboard with them. It keeps them occasional. I eventually decided that it earns the right to do them.
There's a stonking implausibility in two characters having identical DNA even though they were born 450 years apart. If one generation lasts 25 years, that's eighteen generations and their shared DNA wouldn't be four parts in a million even if one was a direct ancestor of the other. There's a plot reason why something like that was necessary, though.
I don't really have anything else to criticise, though. It's a good, solid all-round show. Its ending promises a Season 2 and I'll be peeved if we don't get one. I like how scummy and selfish the U.N. can be. Perhaps it's a bit slow in the early episodes, but I got into it later on as I got fond of the characters. The silliness in ep.23 (and dragging in SPOILER right at the closing credits) is both lovely and important, I think. I've no idea what hardcore mecha fans think of this show, but personally I'd recommend it to almost anyone. I enjoyed it, after all.