Both Castle and House are sequels to Jones's classic, Howl's Moving Castle. However, since much has been said about Howl already, both are set in different kingdoms not explored in the original novel. Both, as well, feel very different from the original.
Castle in the Air was the first sequel to Howl, coming out in 1990 and was set in a southern kingdom not really even referenced in Howl. Our hero is a young carpet seller in this Arabian Nights-themed kingdom who comes upon a magic carpet. He discovers that falling asleep on it causes it to take him to the castle of lovely young princess named Flower-in-the-Night who he, of course, falls head over heels in love with. Since this is a novel, though, things go horribly wrong when flower is stolen by an evil djinn and Abdullah, our young carpet peddler, is suspected of the crime and must go on a quest to find her again.
Although I enjoyed it, this sequel felt quite weak to me. None of the characters were quite interesting to me and the only real high points were when characters from Howl made an appearance. The plot was definitely quite original but it lacked the charm of Howl and was just simply not enough to make it truly special.
The second sequel to Howl, House of Many Ways, did not appear on shelves until 2008, a full 22 years after the original. Charmain Baker, a young girl raised to be very proper in the northern kingdom of High Norland, who finds herself suddenly the caretaker of a distant relation's house while he is away due to illness. Of course, that relation also happens to be the royal wizard and Charmain finds herself trying to navigate a labyrinthine house, dealing with disgruntled kobolds and putting up with some new acquaintances. And, naturally, a few of our old friends make guest appearances.
It seems really unsettling to have such a large time period between the first two books in the series and the last. Of course, House was not supposed to the last book, Jones wanting to write more but she was unfortunately taken away from us in 2011. House, however, is a fitting ending to the series. Charmain is a strong female character, if not quite up to par with Sophie. Along with Peter, her other house guest, they make an interesting pair with their contrasting strengths and weaknesses. While perhaps not being quite as lovable as Howl, House is definitely a worthy sequel.
Both books are quite charming, if perhaps not quite to the standard of the first. The problem is that Howl was just a really stunning book, a nice mix of clever writing, a surprisingly intricate plot and some lovely characters. The other books just couldn't quite revive the formula. They are nice, however, and will answer your questions as to what happened to the old gang after Howl ended. And do you really want to miss Howl disguised as a three year old boy? No, no you don't.