神(かみ)のみぞ知(し)るセカイ(The World God Only Knows) is a series about a dating sim gamer who has been tasked by Hell to rid girls of escaped souls from Hell. If he doesn’t do his job then he gets decapitated! Despite how that sounds, the series is mostly comedic and has a more light-hearted tone.

The anime doesn’t adapt the entire manga. This is most obvious at the start of Megami-hen which skips forward from the end of KamiNomi2 to the Goddess arc in the manga.
Besides this, the anime ends at Megami-hen and doesn’t adapt the rest^A). This, interestingly, leads the anime to having a sad ending.
I’ll elaborate on this a little later.

Comparing the Anime to the Manga: the Manga has better comedic timing, if that even makes sense. Generally, the comedy in the Manga is handled far better - the framing, layout and such all aids it. The exception to this would likely be ‘I am your husband’s illegitimate daughter.’ where the Anime is superior.

The Manga has a bad and abrupt ending. I may elaborate further, but this is the short of it.

Hell has a bit of a problem. Occasionally, a spirit being tortured manages to escape. After escaping, these spirits hide in the gaps of people’s hearts, usually girls for whatever reason.
To reclaim the runaway spirits, Hell formed a team to capture them. This team then forms pairs of people (1 demon and 1 human) who have to the task of finding and capturing the spirits.
The human in the pair is tasked with filling the gap in the hearts of others, while the demon actually seals the spirit after it gets pushed out. Not all pairs work this way though.

I believe it would have been interesting if the conquest targets didn’t lose their memories after the conquest. I don’t necessarily mean that they literally remember everything but that they still have feelings left-over.
The series did, at some point, imply this was the case - although this turned out to be setup for Megami-hen.
This isn’t a flaw with the series; just something I thought would have been interesting.
The conquest targets having some memories left-over could have led to some more interesting situations - for example, Keima could have gotten their help in other conquests.

It should be noted that I do know the reason why this wasn’t present in the series…or, rather, I have a pretty good idea why. I’ll elaborate on that later.

KamiNomi has some influence from Greek and Roman mythology. For example, all of the goddesses have Roman names: Diana, Apollo, Mercury, Minerva, Vulcan. They’re even called the ‘Jupiter Sisters’.
Though it should be noted that outside of aesthetic similarities, KamiNomi is very disconnected from Classical Mythology.

The review should have mentioned that the Manga’s ending is just bad. This section exists so that I elaborate on that.
That doesn’t mean right now.

• Official Anime Site
• The Wikia - Pretty bad, don’t bother.