Near the end of Kirby's tenure at Marvel, he pitched a new Inhumans series in which he planned to introduce new characters, for which he would receive a portion of profits from their use. However, Marvel wouldn't change the terms of his contract, so instead, Kirby launched the Inhumans feature in Amazing Adventures and then left Marvel after the second issue.
Kirby opened the series with the Inhumans being tricked into going up against the Fantastic Four, but when Roy Thomas, Neal Adams and Tom Palmer took over the title, it quickly became about Maximus once again assuming control of the Inhumans -- this time through the use of his newly rediscovered mental powers.
The Avengers helped put Black Bolt back in charge while they were in the middle of the Kree-Skrull War.
Another notable occurrence took place in 1973's Fantastic Four #132 (by Roy Thomas, John Buscema and Joe Sinnott), where Thomas explained away the awkward little facet of Inhuman society that they basically had slaves called Alpha Primitives working for them. The Alphas were freed in this issue, because, well, come on, that was just gross.
Crystal ended up marrying Quicksilver soon afterward.
The Inhumans then received their own series in 1975, with Doug Moench and a young George Perez as the creative team for most of the run. Here, the Kree showed up and worked with Maximus to rule the Inhumans. Eventually, though, Black Bolt and the Royal Family took control of their people once more.
The next major event in the life of the Inhumans was when Black Bolt transported the entire Inhuman home on Attilan to the moon in 1982's Fantastic Four #240.
Then, in Fantastic Four Annual #18 (by John Byrne, Mark Gruenwald, Mark Bright and Mike Gustovich), Black Bolt and Medusa were finally married. (It's shocking they took so long; Marvel had been treating them as if they were married for many years before this issue.)
The next major event of the 1980s for the Inhumans was a graphic novel written by Ann Nocenti in which Medusa and Black Bolt were actually exiled when they decided to have a child even after the Inhuman council determined that Black Bolt's genes were just too worrisome for him to reproduce.
Eventually, though, by the mid-1990s, the Inhumans were back to their normal status quo, although with Crystal having left her family to join the Avengers (she took along her daughter and her Inhuman nanny). But that status quo was about to be thrown out of whack.