"Judge us not by our methods, but by what we seek to accomplish."
- The Illusive Man, Mass Effect 2
The idea of Cerberus was born in the aftermath of the First Contact War, a short skirmish between the human Systems Alliance and the turian Hierarchy that served as humanity's first contact with an intelligent alien species. When the turians laid siege to the human colony world Shanxi, several human mercenaries joined forces with the Alliance troops to fight back against the alien invaders.
Three of them (Jack Harper, Eva Core and Ben Hislop) were captured by the invading forces, brought to Palaven as prisoners of war, and became embroiled in the turian general Desolas Arterius' plot to use an alien artifact on Shanxi called the Arca Monolith to transform the turians into a race of evolved supersoldiers, hoping to harness the power granted by the monolith to stamp turian dominance upon the rest of the galaxy.
However, the Monolith seemingly possessed a mind of its own, and when Desolas' control over it slipped and it seemed as though the Monolith would corrupt and destroy the entire turian race, Harper convinced Desolas' brother Saren to destroy the Monolith with an orbital strike.
In the tussle to escape from Palaven, both Core and Hislop were killed, and Harper barely escaped with his life. Having traveled to several alien worlds, from Omega to Illium, Harper realized that the galaxy may have been a treasure trove of knowledge and wealth, but it was also a very dangerous place for humanity.
Disappointed by what he saw as the Alliance's policies of appeasement towards the Council, he decided that humanity needed a strong voice to defend its interests. He composed an extranet message to several prominent human leaders, politicians and businessmen urging them to join his cause in the creation of a paramilitary organization devoted to human interests above all others.
The Alliance attempted to trace the source of the message, but it was too well encrypted for them to succeed, following which they referred to its unknown sender as "an illusive man" in press releases. The name stuck, and Harper adopted the identity of the Illusive Man to lead Cerberus.
The organization is funded by a vast array of human organizations, both knowingly and sometimes unknowingly, in addition to the Illusive Man's own investment projects. It has been described as having very deep pockets, with the loss of billions of credits being a drop in the ocean at best.
The scientists, soldiers and leaders who make up the Cerberus workforce all join for different reasons: some like Paul Grayson are attracted by the lucrative salaries, some like Kelly Chambers join because they believe it's the patriotic thing to do, some like Jacob Taylor join out of disappointment with the Systems Alliance, and finally some like Kai Leng join out of simple xenophobia and hatred of aliens.
Taking place after Shepard's death at the hands of the Collectors before the beginning of Mass Effect 2, Cerberus operative Miranda Lawson rescues Liara T'Soni from an ambush by the Blue Suns mercenary group, and then fills the asari researcher in on the Shadow Broker's plan to sell Shepard's body to the Collectors for their experiments.
Liara talks to the Illusive Man, who asks for her help in recovering Shepard's body for two reasons: firstly, the difficulty involved in Cerberus trying to contend with the Shadow Broker out in the lawless, unstable Terminus Systems; and secondly, Liara's personal stake in saving her friend's remains from the insidious Collectors, which the Illusive Man saw as something that would drive her to succeed where others with no stake in the matter might fail. Liara agrees to help, not for the Illusive Man's sake, but for Shepard's.
After recovering Shepard's body, Liara hands it over to Miranda, who then proceeds to start Cerberus' clandestine Project Lazarus: the first ever medical resurrection.
The New Shadow Broker
Cerberus took a keen interest in Liara T'Soni's assumption of the mantle of the Shadow Broker, after she and Shepard raided the Broker's base on Hagalaz and eliminated him.
To that end, the Illusive Man had Liara's operations center on the Broker's ship bugged, and listened in on several classified conversations.
One conversation in particular, between Liara and Admiral Steven Hackett regarding anti-Reaper strategies, caught his attention. When Liara headed to the hanar/drell city of Kahje to investigate underwater Prothean ruins, she was attacked by Cerberus Phantoms. After killing them, she was contacted by a hologram of the Illusive Man, who claimed that the Phantoms who attacked her were rogue elements within Cerberus --- operatives who let their fear of the upcoming Reaper invasion get the better of their common sense ---- and that they would be reined in.
He suggested that Cerberus and the Shadow Broker pool their resources and information together to combat the Reaper threat. Liara then invited him to share his information first, correctly surmising that he didn't have any and was simply looking to take advantage of her perceived naivete. The Illusive Man warned Liara that she was out of her depth and that word was spreading within the Terminus Systems that the Shadow Broker was slipping up, but Liara disconnected his call and prepared to leave Kahje for the Prothean research center on Mars, where Shepard finds her at the beginning of Mass Effect 3.
Before the beginning of Mass Effect 3, the Illusive Man dispatches two of his most trusted operatives, General Oleg Petrovsky and Colonel Raymond Ashe, to wrest control of the space-station Omega away from its mobster queen Aria T'Loak. To do so, they secretly dump genetically modified creatures called Adjutants --- the result of Cerberus' experiments with the Reaper technology salvaged from the ruins of the Collector base beyond the Omega-4 Relay ---- onto the streets of Omega, leading to widespread panic and countless deaths as the creatures kill civilians and mercenaries alike, converting their corpses into more Adjutants.
Petrovsky lures Aria away from Omega under the pretense of cutting off the Adjutants at their source, while Ashe takes advantage of her absence and the dysfunction it creates to bring in Cerberus troops, quell the warring gangs, and assume total control of the station. When Aria returns, Ashe releases an Adjutant inside Afterlife. Aria manages to kill it, but not before it infects Ashe and he starts to transform into an Adjutant.
Before the transformation is complete, Petrovsky executes Ashe with a bullet to the head, and then warns Aria to leave Omega or he will have the entire station bombed to rubble by the Cerberus fleet waiting outside. Aria leaves Omega in Petrovsky's hands, vowing to eventually return and take back her kingdom.
Cerberus is introduced for the first time in the 2007 video game Mass Effect, though the organization is not explored in much detail, being primarily the focus of a few side-missions. Shepard learns of the organization's human-supremacist leanings through personal experience after encountering Cerberus squads and research facilities, as well as the accounts of Alliance officials like Rear Admiral Kohaku and Corporal Toombs.
The latter alleges that Cerberus was behind the notorious Akuze massacre, having lured thresher maws to the helpless colony to observe the creatures' behavior. Hearing this, Kohaku purchases information from the Shadow Broker about the organization's origins, resulting in his assassination by the group.
Shepard mostly encounters scientists and soldiers working for Cerberus, with no word of the organization's leadership or hierarchy.