Terran Empire
The Terran Empire is, in the fictional universe of Star Trek, the Mirror Universe counterpart of the United Federation of Planets. It appears to differ from the Federation in almost all ways — where the Federation is peaceful, the Empire is violent to the point of allowing promotion in its Starfleet via assassination of superiors; where the Federation has strict rules protecting less-advanced societies, the Prime Order of the Empire is to allow no resistance to its wishes to go unpunished. Punishment on Imperial Starfleet vessels is administered by the use of hand-held agonizers or, for serious offenses such as an unsuccessful assassination of a superior, the agony booth. Both of these work by direct stimulus of the brain's pain centers. Aliens are experimented on in painful ways as a matter of routine.
The uniforms and heraldry of the Empire reflect its very violent nature; uniforms are more flamboyant and often blatantly sexually suggestive, and always incorporate weapons — daggers and phasers. The symbol of the Empire is a stylized Earth with a sword behind it, the hilt appearing to protrude from the North Pole and the point coming out behind the South Pole. Assassination of disobedient officers by their subordinates is encouraged as a means of maintaining discipline and as a means of career advancement for those who are successful. As such, high ranking officers typically have bodyguards to counter such attempts. A starship commander will typically keep one, or even several, consorts from among the crew, although these relationships tend to be brief - given the Empire's tendency towards treachery and betrayal.
The Empire is stated to be unstable in the episode in which it appears ("Mirror Mirror") and the mirror-universe Mr. Spock estimates that it will be overthrown, violently, in the next few centuries. In contacts with what appear to be that alternate history in later Star Trek series, this appears to have taken place. In the Star Trek: Deep Space Nine episode "Crossover" we discover that it fell to an alliance of Klingons and Cardassians, and Humans and Vulcans are now enslaved. (However, given that there are an infinite number of universes, logically some of these will contain a Terran Empire that never fell...)
The specific point at which the Mirror Universe deviated from the normal Trek universe is unknown. The opening theme from the Star Trek: Enterprise episode "In a Mirror, Darkly" has lead many to believe that the Empire existed at least as early as the Project Apollo moon landings (an astronaut is seen planting the Empire's flag on the moon). However, it is possible that was not the Apollo mission, simply another mission to the moon, perhaps the founding of a lunar colony. It is known that first contact with the Vulcans in that universe proceeded very differently, as an angry mob of humans stormed the Vulcan ship, killed its crew, and took their technology. Also, in 2155 Mirror-Archer mentioned that the Terran Empire had already endured "for centuries".