It's the latest anime from Natsume Akatsuki, the man behind KonoSuba (which I love) and Kemono Michi (which is more problematic, but I like that too). He has a distinctive style of comedy, which can be summarised as "useless scumbags". Each of these shows has a piece-of-shit male character who creates half his own problems and has unwillingly acquired a party of female associates who are similarly dreadful. They'll screw up, forget important things, leave their comrades in the lurch, be perverted and/or have extreme personality issues. The gang abuse each other non-stop and are generally about as trustworthy as a scorpion in your shoe, but in a pinch will generally pull together to help each other.
This particular anime takes the scumbag principle to the next level by having heroes who work for an evil organisation. They've been sent to this planet in order to help invade it, with which they're completely okay. Furthermore, the Kisaragi organisation has an internal reward scheme for bad deeds. Do something noble and you'll lose Evil Points. Kicking puppies, molesting women and pushing children off bridges will gain you Evil Points that can be traded in for guns, armour, pornography or whatever else floats your boat. (Who programmed the AI that judges this? It's an amazing technical achievement, in its utterly pointless way.)
Oh, and Kisaragi's bosses (named after Biblical demons) are all female, yet they're happy with this Evil Points system that encourages sexual harassment and worse.
COMBAT AGENT SIX = a massive and occasionally off-putting pervert. He's an idiot. He regularly does things so scuzzy that all his friends cringe. He's been surgically enhanced for combat, but he can't even remember his own name. On the upside, though, he has a vestigial conscience that activates in genuinely grim situations and he wouldn't kill or abandon his comrades.
ALICE KISARAGI = Six's android assistant, in the form of a little girl. She's useless in combat (unless you give her a gun) and she's even more rude and heartless than Six, but she's also the cleverest person on the planet.
NATIVES OF THIS UNNAMED PLANET
SNOW = commander of Princess Tillis's Royal Guard. She's the sexy one. Big boobs and cleavage, but she's also an incompetent who's obsessed with honour, swords and money.
ROSE = a magical creature with mismatching eyes and the ability to absorb the abilities of whatever she eats. She loves eating. If you're stuck in the desert and your supplies have run out, watch her closely. That said, though, she's the show's nicest and most enthusiastic character. (The early episodes give her a chuunibyou surface personality, but this isn't very interesting and the show almost immediately forgets about it.)
GRIMM GRIMOIRE = priestess of the chaos god Zenarith. Goes around in a wheelchair and casts curses on people that backfire on Grimm herself 20% of the time. She's also a clingy man-chaser. (They all avoid her.)
This is funny, but it's not for everyone. Natsume Akatsuki likes it near the knuckle, with threatened sexual assault that we're meant to think is humorous (ep.5) and a tiger man who likes small children too much (ep.12). I lost patience with Princess Tillis and her dad refusing to shout "penis festival". Yes, Six was being puerile when he chose those words, but they'd unlock the water supply for a desert kingdom at war. Swallow your pride and say the damn password. Yes, I realise it's another instance of Akatsuki Scumbag Humour, but for me it undermined the plausibility of the setting.
The show's also often unwatchable if children are present. Kazuma was sleazy sometimes in KonoSuba, but it's a great children's show if you skip the succubus episode (ep.9). Kemono Michi is all about near-bestiality and humiliation, but you wouldn't be grabbing the remote control if someone was about to catch you watching it. This show, on the other hand, is full of hair-raising behaviour, usually performed by Six and encouraged by Alice. It's usually funny, but good grief. That said, though, actual sex is one of the lines that our heroes never cross (despite their often groin-driven behaviour). Just as Six doesn't want to kill or eat anything sentient, he also has no romantic interest in the girls around him. Grimm he regards as a clingy nightmare and over the hill, Snow has personality issues, Princess Tillis is a black-hearted schemer, Rose is underage and Alice is even more underage (and an android who's incapable of sex anyway).
While some may say Six has a harem, it's more of an anti-harem in his eyes. All of his party members outside of Alice have some major personality-based deal-breaker for Six. Grimm is too clingy, Rose is just a kid, and Snow is too greedy for her own good. But for Alice, it's the opposite. Her personality is a perfect match for Six—it's the fact her android body looks like a child's that turns him off.
It's also worth noting that, underneath, the show has a serious core. Snow, Rose and Grimm all have borderline tragic pasts. The kingdom is under attack by demons and there's clearly some backstory and worldbuilding we haven't been told yet. (Magic vs. science, for instance.) There's a logical reason why almost everyone's female (most of the men died in the war), which is unusual in anime. Twice a season (ep.6 and ep.12), things get bad enough that the drama gets real and people are forced to make real choices. Those are the best episodes, incidentally. Those are when our anti-heroes get heroic.
Oh, and I love the theme songs.
This show will absolutely, definitely not work for everyone. Its humour runs on idiots acting dreadfully. I wasn't keen on every episode, e.g. ep.8, ep.10. If you can get over the worst of it, though, there are a lot of laughs in here and I'd love to see a second season. It probably depends on how likeable you find these very dreadful people. Underneath, there's good in them.