Warning: Symphogear spoilers. Not that it really matters, because this show transcends mere plot.
The very first thing Symphogear does is lie to its audience.
Symphogear, or to give the show its ridiculous full title Senki Zesshou Symphogear - Meteoroid-falling, burning, and disappear, then..., is best described as Macross meets magical girls; a number of young women are given ancient magical relics which enable them to use songs as armour and weapons to fight the alien threat Noise.
The show appears thematically dense on a surface level. All the terminology is music- or sound-related, and there's some strong imagery in the idea of humanity's heroic melodies defeating the monstrous Noise. But, like KILL la KILL, none of these apparently important references actually mean anything to the... well, calling it a story might be overly charitable.
The biggest problem Symphogear has is trying to decide what it wants to be. None of the masks it tries to wear really fit convincingly, but it's so earnest that I couldn't help but love it for trying so hard.
It has one of the most obvious yet most understated gay relationships in anime. It has characters who sing their feelings while battling each other. It has full-screen, comic book-style freeze-frames for special attacks. It has a story about the genetic reincarnation of an ancient priestess trying to rebuild the tower of Babel so she can destroy the God who lives in the moon. It's a mess of ideas that never quite work the way you feel the writers and animators intended (hoped?), but still somehow I can't help but cheer for it.
Symphogear's whole first series is building towards an ending that's promised by the opening scene of the first episode - a lie that I bought into. Having that scene constantly in mind, particularly as the finale approached, gave much of the story more dramatic heft than it might have otherwise had. It's constantly pulling off a balancing act between the ludicrous spectacle of the Symphogear battles and the difficulties Hibiki has keeping this new superhero work secret from her girlfriend Miku. And with the implication that Hibiki wasn't going to survive the series, I was more worried about whether they'd part on good terms than if they'd defeat Finé.
The second and third seasons have altogether different problems.
Season two, Senki Zesshou Symphogear G: In the Distance, That Day, When the Star Became Music..., decides to jettison all the character stuff that made the first interesting and just turn the Symphogear to eleven. It's total nonsense, spectacle for its own sake, with a terrorism subplot that follows three new Symphogear users who all but have "eventual hero" tattooed on their foreheads. Hibiki and Miku's relationship, the beating heart of the first series' plot, is all but ignored for two thirds of the running time. The transformation sequences from the first season - quick, incredibly cool and highly stylized - are replaced with more... traditional fanservice-based sequences.
The third (and so far final) season - Senki Zesshou Symphogear GX: Believe in Justice and Hold a Determination to Fist. - swings almost too far the other way, with a plot that's somehow both complicated and dumb at the same time, and much lower-key battles. The fanservice is turned up uncomfortably higher. The primary emotional storyline involves Hibiki trying to figure out what to do about her deadbeat father.
To call Symphogear a disaster would not be inaccurate, though I do think it would be unfair. The first season, inconsistent as it is, still has a strong core and some great ideas that a more polished show might not take risks with.
I couldn't recommend watching the whole saga (though with a fourth season constantly rumoured, you might do well to catch up!), but the first 13-episode series is definitely worth your time.