As a whole (Fantastic Four #45, 1965)
Their goal was apparently twofold — to investigate possible ways of circumventing their own evolutionary stagnation, and to create a powerful mutant race of soldiers for use against the Skrulls. However, although their experiments were successful in creating a strain of humanity with extraordinary abilities, the Kree abandoned their experiment for reasons which are not yet clear.
Their test subjects, the Inhumans, went on to form a society of their own, which thrived in seclusion from the rest of humanity and developed advanced technology. Experiments with the mutagenic Terrigen Mist gave them various powers, but also caused lasting genetic damage and deformities. This led to a long-term selective breeding program to try to mitigate the effects of these mutations. Their city Attilan has frequently been relocated and, as of 2005 stories, rests in the oxygen-bearing Blue Area of the Moon.
The once-secret existence of the race has come to light among the general public as the Inhumans interact more often with many of Earth's superheroes — including the Fantastic Four, the Avengers, and the X-Men — whom they have aided against threats such as Galactus, Ultron-7, Magneto, and Apocalypse.
The Inhumans are led by their king, Black Bolt, and his royal family, consisting of Medusa, Karnak, Gorgon, Triton, Crystal, Maximus the Mad, and the canine Lockjaw. Both Crystal and Medusa have been members of the Fantastic Four; Crystal has also been a member of the Avengers.
One interesting observation is that Attilan's society and culture are predicated on a conformist belief system which permits individuality as it applies to genetic development and physical and mental ability, but demands rigid conformity in that each member of society is assigned a place within that society according to those abilities following exposure to the Terrigen Mist. Once assigned, no Inhuman, no matter how great or powerful can change their place within this rigid caste system.
Another interesting note is that the Inhumans' culture strictly prohibits miscegenation between Inhumans and other races. Although a member of the royal family, the Inhuman Crystal appears to have ignored this prohibition married outside of her caste to wed the mutant Quicksilver. However, this may be a privilege due to Crystal's standing as a member of the royal family.
In contrast it appears that such permissive behavior is lost on the children of the immediate members of the royal family. Gorgon's daughter, for example, attempted to form relationships outside of her caste and was strictly prohibited from doing so, although this may have been because her relationship was with an Alpha Primitive, the lowest Inhuman caste. It is not clear, however, whether commoners face such strict disciplinary measures under similar circumstances.
However, Inhuman society changed radically recently. Ronan the Accuser sought to use the Inhumans as an army to disrupt the Shi'ar control of the Kree after their defeat in the Kree-Shi'ar war. Appearing over the city of Attilan, Ronan seized control in a surprise attack and forced the Inhumans and their king, Black Bolt, to obey, or he would destroy their only home and everyone in it. During their time in forced servitude, Ronan revealed that the Inhumans had always been intended as weapons in service to the Kree. To this end, much of the genetic attributes that were encoded in them during the original experiments were meant to give them the abilities and appearances of various alien races. The idea being that these Inhuman slaves could be used to infiltrate alien worlds and races to conduct espionage or assassinations to weaken potential conquests. Ronan used the Inhumans in just this manner, disrupting treaties being negotiated by the Shi'ar, and launching attacks on ships and bases. Eventually, Black Bolt sought to free his people by challenging Ronan to a personal battle. If Ronan won, the Inhumans would continue to serve him. If the king won, the Inhumans would go free. After a terrible battle, Black Bolt won and Ronan, demonstrating that the Kree still had honor, kept his word and left the Inhumans. All was not over however, as the Inhumans were not willing to just follow Black Bolt back to Earth. Pressure had been building in the closed society of Attilan since open contact with the outside world had been made. During their enslavement by Ronan, the Inhumans had wished for their freedom, but had also developed a sense of pride in their power and a belief in their own destiny. They no longer believed that Black Bolt or the royal family was fit to lead them in the new life they wanted, and they exiled the royal family from Attilan. The royal family returned to Earth to find their destiny. After suffering bigotry and living in Latveria, they returned to Attilan which was located on the Blue Area of the Moon. The Inhumans are currently fostering better relations with Earth by sending students to a Wisconsin University.In the events of Son of M, Quicksilver stole the Terrigen Crystals in an attempt to give himself back his powers, and to give back the de-powered mutants from M-Day their powers. The theft led to a conflict on Genosha between the re-powered mutants (whose powers came back as too powerful for their own good, and eventually surrendered), the Inhumans, and the U.S. Office of National Emergency. The conflict ended with the O.N.E. confiscating the Terrigen crystals, to which Black Bolt then verbally declared war on the United States.