in the Pre-Crisis/Post Crisis Continuty, The H.I.V.E. was an organization that trained many assassins and even mercenaries. They sell their services for anyone who can and willing to pay them, the atrocities the H.I.V.E. did made them an enemy of the Teen Titans (and other groups.) They are leaded by Queen Bee and Adeline Wilson.
in the Post-Flashpoint/New 52/Rebirth, The H.I.V.E. is a social media company striving to bring the world together in unity but unknown to the World, They are secretly kidnapping People with psychic powers to use their them and their powers to pave the way for Brainiac's invasion.
The H.I.V.E. Academy was originally owned and lead by the H.I.V.E. Headmistress until its management was taken over by Brother Blood. the H.I.V.E. Academy during the Headmistress management served as a villain-in-training institution that provided "well organized, highly trained, and combat equipped" H.I.V.E. agents for hired as long as they pay them. Cyborg went to the academy while undercover with the alias ''Stone'', When Brother Blood was preparing to mass-country a weapon called Ion Amplifier. after seeing this, Cyborg destroyed the Academy with a Sonic blass augmented by the Amplifier. Brother Blood keep opening the academy at different locations but his plans are foiled by the Titans and he was captured by the Titans themselves at the end.
The H.I.V.E. in Teen Titans Go! is very different from the original series, The Group is called the H.I.V.E. Five, a supervillain group consisted of five members that are Jinx, Mammoth, Billy Numerous, See More. Their only goal is to destroy the Teen Titans, They also rob banks in Jump City.