The Three Families (also known as The Families) were a powerful organisation derived from three different families. They systematically manipulated the human race over the 20th century for their own purposes. It is believed one family was centred on politics, one had entered into the economic world and the other had gone into media. (TW: The Gathering)
History
In 1928, Little Italy, men belonging to the Ablemarch, Costerdane and Frines families purchased the immortal Jack Harkness and took samples of his blood. He later escaped their custody, thanks to the man who had first kidnapped him, Angelo Colasanto. (TW: Immortal Sins) Colasanto's granddaughter later stated the families refused to work with Colasanto because of his homosexual relationship with Harkness. Despite this, he would keep a close eye on the families and Harkness throughout his life. (TW: End of the Road)
Through the 20th Century, the Families would remain hidden, but would manipulate events on a global scale. Their influence was so large that they altered and erased data on a global scale. All factual reference to the families disappeared. (TW: End of the Road)
In 1998, when technology had developed so numerous records could be analysed quickly, they found people living within a two-mile radius of the Blessing in Shanghai lived the exact average lifespan of the rest of the world. The Families discovered and gained control of the Blessing, a secondary pole running through the centre of the Earth, connecting Shanghai to Buenos Aires. (TW: The Middle Men, End of the Road, The Blood Line).
Having discovered the Blessing, the Families set about planning to cause and control what would come to be known as The Miracle, stopping people from dying over the entire planet.
They caused the Miracle in 2011 by simultaneously putting Harkness' immortal blood into both ends of the Blessing. This was only the beginning however; they planned to use their influence and wealth to control the human race. The same day, they sent an email to the Central Intelligence Agency consisting of just one word: "Torchwood". Harkness erased all records of the Torchwood Institute and all of its living members to protect Gwen Cooper. (TW: The New World)
Through PhiCorp, they employed Jilly Kitzinger to tell history the way The Families want.
In September of that year, they intended to seal the Blessing by collapsing the caves at each end, stopping anyone from interfering with it again and negating the Miracle. This was interrupted by members of Torchwood. After a standoff, Harkness and Rex Matheson released Harkness' blood (now mortal due to the Miracle) into the Blessing again, reversing its effects.
"The Mother" of the Families was subsequently killed by Oswald Danes, who blew up himself and the Shanghai complex while holding onto her, in Buenos Aires Rex Matheson killed "The Father" by throwing him down The Blessing. The Families didn't see this as a defeat, more as a trial run; they had a Plan B. (TW: The Blood Line)
Influence
They could do so without PhiCorp CEO Stuart Owens learning of the Families' existence. His own attempts to discover who was manipulating his company were largely fruitless.
The family had high-ranking moles in many organisations, including at least three within the Central Intelligence Agency.