An alien from another planet has been stranded on earth for the past 400 years and finally has the opportunity to return home. His travel plans are upended when an attractive but spoiled actress moves into the apartment next door and begins to invade his life physically as well as romantically.
This is a remake of a 2013 Korean series of the same name and having seen both, some comparisons are worth making. Overall, I prefer this version to the Korean version with a couple of qualifiers. First of all, Korean series have a habit of d-r-a-g-g-i-n-g out the plotline to the point that an enjoyable series becomes a bit irritating. The Korean version is definitely guilty of this. Sixteen plus hours of romantic angst punctuated by comedy tries my patience. The Japanese series tells the exact same basic story in 10 episodes of around 45 minutes each. This does make the Japanese version feel a bit "anemic" when compared to the Korean one but at least it doesn't wear out its welcome.
The main actor playing the alien is good in both series. Kim Soo Hyun and Sota Fukushi are both handsome and charismatic and enjoyable to watch. I do feel that the Korean actress (Jun Ji-Hyun) is just a bit more believable as a glamorous television star than Mizuki Yamamoto. The Japanese actress is definitely cute as a bug's ear and hits all the right comic and tragic notes but ultimately lacks the right look in my opinion.
And if you're looking for an enjoyable science fiction program, I would avoid both series. This is strictly a romantic comedy with a male lead that has some interesting powers (freezing time and moving things about mainly). Very little time is dedicated to his alien background (you only get to see his spaceship one time and the special effects involved are underwhelming).
Bottom line: it's an enjoyable way to pass the time. If you want to spend less time and have the same basic experience, avoid the Korean version and stick with the Japanese one.