New Dalek Empire

The New Dalek Empire was founded by Davros in the aftermath of the Last Great Time War, which destroyed the original Dalek Empire. Davros apparently lost some control of the Empire, which fell under the reign of the Supreme One.

Overview
The New Dalek Empire was somewhat different compared to the Dalek forces that appeared after their empire's supposed destruction in the Time War. They were not survivors using scattered technology but rather a true empire and quite capable of combating Time Lord technology. They were even capable of capturing and disabling a TARDIS. Their forces consisted of hundreds of starships with enough power to devastate the universe. Their central base of operations was the Crucible where they planned to reside on when the reality bomb destroyed the universe.

First Attempts
The New Dalek Empire was to be the new Empire of the Daleks that the Cult of Skaro had planned to create. The very first attempt was on planet Earth with the Genesis Ark, to unlock it and unleash the Daleks within, of which the Doctor thwarted. Time travelling from London in 2007 to New York City in 1930, the Cult, now the last four Daleks in existence, attempted to conquer Earth and recreate the Dalek Empire.

This attempt, even with the help of the Final Experiment (which included use of Pig slaves and human-Dalek hybrids) failed due to the interference of the Tenth Doctor. At the end, Dalek Caan was the last surviving Dalek in all of creation. (DW: Daleks in Manhattan / Evolution of the Daleks)

New Empire
Caan activated an emergency temporal shift to escape the Doctor, and ended up at the Gates of Elysium during the Last Great Time War. Travelling into a time-locked era ruined his mind, but he helped to save Davros from his death. Davros, like the Dalek Emperor who also survived the Time War by time travel, rebuilt the Dalek Fleet of two thousand ships and millions of Daleks - unlike the Emperor, Davros rebuilt the Daleks out of his own Kaled cells. Caan was left as a sort of prophet, and a new Supreme Dalek was created to oversee the Dalek forces.

The Daleks moved 27 planets into the Medusa Cascade from various times and places (mostly mid-2009, but from other eras as well). These made a large device when put together. The new Daleks then took control over the planets in the Cascade, apparently concentrating their forces on Earth. They took many humans aboard their ships, and wiped out any resistance that they met. (DW: The Stolen Earth)

The new Empire planned to use the 27 planets in the Medusa Cascade in conjunction with the Crucible's energy source to power a Reality bomb created by Davros. This would have led to the destruction of all of existence and allow the Daleks to be the sole inhabitants of the universe. However, interference from the Doctor and his companion Donna Noble led to the device being destroyed. Despite this, the Daleks had enough troops and starships to slaughter the universe until they were killed by the New Doctor overloading and feeding back the Dalekanium.

Also, Dalek Caan was in fact working against them and aiding the Doctor, having deemed the entire race evil after seeing what they had done. This act destroyed all the Daleks and their starships which includes the Crucible. Its presumed that the Dalek race were destroyed as a result of this act, although as Caan and Davros were not affected, theoretically there could have been others immune to the effect as well, Davros's chair was of a different design to a base Dalek's, also Caan's armour appeared to have no energy so no 'power feed' could be blasted back. (DW: Journey's End)

A New Dalek Paradigm
A single badly damaged Dalek Saucer with three Daleks onboard survived and fell back through time to World War II. There they found a Progenitor Device, which contained enough Dalek DNA to restore the species. However, as the surviving Daleks were created from Davros' cells, the Progenitor did not recognise their DNA as "true" Dalek, and refused to activate.

The Daleks set in motion a plan to lure the Eleventh Doctor, the one being who could positively identify them, to the same time period. Travelling to 1940, they posed as "Ironsides", the inventions of Professor Edwin Bracewell (who was actually an Android they created and implanted with human memories) and offered to assist Winston Churchill in winning World War II. When the Doctor discovered the Daleks, he attacked them, declaring their true name out loud. The Daleks transmitted this "testimony" to the Progenitor, which accepted their Dalek-ness, and began creation of the new Dalek race. The first act of the new Daleks was to destroy the old ones, declaring them "inferior". The old ones, though, showed no resistance, even declaring themselves inferior. The new Daleks then threatened the Doctor with the revelation that Bracewell contained an Oblivion Continuum bomb, easily capable of destroying the Earth. Although the Doctor managed to disarm the bomb, the new Daleks utilised a Time corridor to escape to the future, in order to begin rebuilding their empire. (DW: Victory of the Daleks)

Possibly apocryphal information
One source states that there were many other survivors from the Crucible who fought the New Dalek Paradigm, claiming that they were in fact the "pure" Daleks as they were the direct children of Davros. (SP: Doctor Who Experience)