How the Federation came to power was never clearly stated in the series, though in the episode "Countdown" it was mentioned that it was formed some 200 years before the main rebel attack on "Control" (see below). The Federation primarily expanded its territory though conquest, enslaving weaker worlds and exploiting their resources to fuel the military. In other cases, the Federation would infiltrate more distant worlds where they would help a local tyrant achieve power or install a malleable ruler (episodes "Bounty" and "Horizon"). These puppet leaders would rule over their own planets, but under the constant shadow of the main Federation and their planets would eventually become part of the Federation. How far the Federation's power spread was never clearly indicated either, as mentioned in the series there were many "neutral worlds" in existence.
The Federation maintained control of its citizens through fear and through dosing the air and water with pacification drugs (episode "The Way Back"). In extreme cases such as Roj Blake's, brainwashing and re-programming were used. In at least one case, a planet was equipped with a radiation bomb that would wipe out the inhabitants in the case of rebellion (episode "Countdown"). In the episode "Horizon", the Kommissar indicated that the incident of rebellion was less than one in 100,000 and that many of these were snuffed out in youth. Despite all these efforts, or perhaps because of them, the Federation was never able to quite stamp out resistance.
The Federation's main seat of power is located on Earth, the capital world where most inhabitants serve with drug-induced loyalty. The Federation was commanded by the President of the High Council, below which was the Supreme Commander, who was in control of the military and Space Command. At the beginning of the series, Servalan held the position of Supreme Commander. Later, when Star One began to break down, she staged a coup and took over as President (in the episode "Star One"). She initially ruled alone, without a High Council or a Supreme Commander. The High Council was later restored (in the episode "Rumours of Death"); the office of Supreme Commander was offered to a Space Commander if he captured the Liberator, in the episode "Volcano", but this attempt failed.
Federation law was strict and punishment severe. Crimes were rated by category. For instance, the unauthorized leaving of the main city complex on Earth was a Category-4 infraction. Category-9 crimes, such as child molestation, (of which the series' main protagonist Roj Blake was accused), was stated by the arbiter at Blake's trial as the most severe. In any case, criminals were commonly tried unfairly in Federation courts, where a list of mock charges were sometimes added to a defendant's original charge. Sentences were typically life imprisonment, torture and/or execution. Probably the worst fate would be "re-education" under the pacification programme. If the Federation saw use for keeping the criminal alive, they would undergo brainwashing in an attempt to reform them into content citizens and put them back into society as mindless slaves.
First mentioned in "Seek-Locate-Destroy" and first seen in "Duel", Mutoids (see below) were one of the most extreme forms of brainwashing. The subject's mind was rebuilt completely so that their only desire was service to the Federation.
Religion of any form is also known to have been eradicated under Federation law ("Pressure Point"). Possibly because of this, the Federation had changed the Earth's Gregorian calendar (the so-called "Old Calendar") to the "New Calendar" for date keeping. In the first episode "The Way Back" a date was given as "52.6.8" suggesting by the New Calendar the year was either 152 or 252. It is uncertain when the "New Calendar" was set in place, but it was possibly established at the founding of the Federation.
Edit: In the episode Cygnus Alpha Blake hints that the Federation started shipping prisoners to the penal colony 200 years ago and Vargus is the 5th gen of a first batch of prisoners, Vargus says, "And it was my great, great Grandfather who found a way to unite them..." So Blake's 7 is set in the 3rd century of the second calendar at least as far as the series hints at. And according to the episode Killer humans had been travelling in space for at least 700 years. The entire series spans a time period of at least 5 or 6 years set at least 700 years plus into the future.
The Federation apparently had the mightiest military force in the galaxy and it used the threat of invasion to intimidate non-aligned worlds. Occasionally the Federation might employ more subtle methods of taking over worlds, such as installing puppet governors under their control, supporting revolutionary forces loyal to their cause, and inciting wars between worlds by manipulating delicate political issues. In the latter case, if war broke out between worlds, the Federation would enter as a neutral arbiter and peacekeeping force making it easier for eventual take over.
The Federation military was made up of troopers who wore a black uniform, sometimes with silver trim, and helmets with masks to hide their faces. The Federation logo was prominently featured on the upper left side of the uniform. They were issued "paraguns", a kind of handheld gun, however, when fired, sparks and smoke would exit the barrel, suggesting it fired a kind of projectile, or possibly a small packet of plasma, although the gun's report sounded nothing like a conventional firearm.
The Federation also used special soldiers called "Mutoids" who were humans that had undergone a special conditioning to make them absolutely obedient to their handlers and part of the conditioning involved the removal of all memory of their past lives. They functioned as pilots, technicians, bodyguards and shock troopers. Mutoids appeared to be mostly female and wore the same uniform as troopers except for a characteristic black skullcap on their heads which possibly housed cybernetic components and may have been directly attached to their bodies as part of their conditioning. Mutoids were also required to consume a "blood serum" to stay alive and this led to the belief by some in the Federation that they were vampires. The blood they consumed could be taken from a captured victim using a wrist mounted device that extended a tube and syringe. In the episode "Duel", the Mutoid who accompanied Travis attempted to drain Jenna of blood before Travis ordered it to stop. It was also suggested that the mutoid's obedience and loyalty might come into question if it did not properly feed in time.
Federation officers appeared to have no standard uniform design, although they typically wore black. They were seen throughout the series in varied styles of dress that differed between episodes. Troop commanders and ship captains typically wore similar-looking uniforms as their subordinates.
The Federation naval fleet was composed of various types of ships of varied design, however the most commonly encountered by Blake and his team were dark-red bullet-shaped craft called Pursuit Ships. Travis had taken command of the latest version, the Starburst-class, which were the only ships with a top speed capable of keeping up with the Liberator. In later seasons, Tarrant identified the attacking pursuit ships as "the new mark fours" which appeared identical to the Starburst-class, yet apparently more advanced and maneuverable. Individually, the ships were no match for the Liberator which often destroyed them with a single shot from her neutron guns. However the attacking ships usually ganged up on her with plasma bolt volleys which could easily cripple Liberator once her power reserves ran down. This often forced Blake, and later Tarrant, to come up a clever tactic to save the ship when retreat was not an option.
President Servalan was seen using several kinds of ships throughout the series. In the third season she used an organic-looking black cruiser that looked nothing like the Federation pursuit ships, or anything built by humans, and appeared almost alien in design. It had a mouth-like opening on the front that could swallow ships, as seen in the episode "Children of Auron" when Servalan captured an Auronar pilot. The craft appeared shortly after the fall of Star One and the intergalactic war with the Andromeda aliens. Because the Federation had reportedly lost so much of its fleet in that battle, the ship might have been a captured spoil from that war. The ship could land, as seen in the episode "Moloch". In the episode, a renegade Federation commander planned to use alien technology to replicate copies of the ship to replace his lost fleet, suggesting it to be a valuable warship. The ship was later destroyed on Terminal when a creature native to that planet entered the landed ship and triggered a self-destruct device.
In the final season of the series, Servalan, (now known as Sleer), used a stylish-looking white ship, with black and red stripes, that also could land as seen in the episode "Animals".
In the episode "Sand", Servalan was aboard a yellow ship with landing capability, suggested to be a scout vessel, that has the logo of the Federation emblazoned on the side.
The Federation is the main adversary of Roj Blake, captain of the Liberator and the ad-hoc leader of a small group of rebels who oppose Federation rule. Blake - an outspoken rebel - was captured and tortured for spreading sedition. His family was also executed for his crimes, but instead of executing Blake, (and making a martyr of him) the Federation tried to brainwash him into a content citizen. Blake later overcame the brainwashing, remembered who he really was and what the Federation had done to him, and vowed to bring them down and free the galaxy.
The Federation maintains its power from an automated computer control centre known as Star One, which is not only the nerve centre of the military network, but also monitors political situations and intelligence. Star One also controls all aspects of Federation life, including deep space computer flight coordination, global climate control on Federation worlds, and communications relays. Although Star One is well defended, it is the Federation's "weak spot", for if it were ever destroyed, the Federation would break down and could be easily overthrown, thus finding and destroying Star One was Blake's primary goal throughout the second series. This Federation facility, also known as "Control," was originally located on Earth. Blake originally targeted this terrestrial facility, but found that it was a decoy upon penetrating it. Blake then learned it had been moved to a secret location thirty years beforehand ("Pressure Point").
In the episode Star One the crew of the Liberator find the control centre, but they also find that it controls a vast space minefield that protects the Federation against the Andromedans. Its systems are destroyed by infiltrating Andromedans and the Liberator makes a stand to protect humanity while Federation ships race to the battlefront.
After the destruction of Star One and the loss of 80% of their fleet in the Intergalactic War, the Federation fell apart. However, by the fourth series, the Federation was regaining power due to new mind-control drugs ("Traitor"). Servalan, under the alias Commissioner Sleer was slowly regaining her power. However in the penultimate episode ("Warlord") Avon unites the various anti-Federation resistance groups and gives them the antidote to the mind control drugs leaving the fate of the Federation uncertain.