Tatsumi is one of my favourite smart arses ever, period. GK follows East Tokyo United (ETU) the main characters at the start are Takeshi Tatsumi, their new coach, Murakoshi their aging captain and the man credited with keeping ETU together, and Tsubaki a youngster who's in his first year of pro football. Tatsumi is a former Japanese national and East Tokyo United (ETU) player. At the start he is thirty-five and has spent the last two years coaching an amateur English football team which ends up in the top 32 of the FA cup. After their dramatic loss, he is recruited as the manager (coach / manager are used interchangeably, something to keep in mind) of ETU, his old club in which has been struggling since he left. Tatsumi says 'yo I'm back bitches and we're gonna show Japan how amazingly good ETU is'. Sadly he doesn't use these exact words.
So GK follows ETU as Tatsumi builds his team and prepares to shit all over the competition (again, not really). Murakoshi in particular is resentful towards him, he's called Mr. ETU for a reason! Tsubaki is the shy yet talented youngster who Tatsumi believes in, despite all the mistakes he makes, all the team gets fleshed out with their personalities and weaknesses. People love Giant Killing so much because it isn't a fairytale 'talented school team win the national cup' type story, in GK they lose. A lot. Tatsumi is happy to let them loseso long as they gradually come to understand him, and each other. After all, you play your best when you're having fun! I forgot to mention this, another unique thing about GK is that it not only follows the team, it follows the fans young and old and even a freelance journalist.
TL;DR: It's a unique sports manga where they don't magically win through the power of friendship, they lose and they need to lose all orchestrated by Tatsumi who is so annoying and yet so brilliant. There is no single main character, there are several and even the background ones get fleshed out wonderfully.
Excuse the wall of text, I get pretty passionate about GK.