New Dalek Empire

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

Overview
The New Dalek Empire was very different from the prior Dalek force that was reconstituted by the Dalek Emperor after the Time War. The prior force was full of insane hybrids. (TV: The Parting of the Ways) The New Dalek Empire, however, was dramatically larger, and quite capable of combating even Time Lord technology: they could capture and disable a TARDIS. Their forces consisted of hundreds of starships with enough power to devastate the universe. Their central base of operations was the Crucible, on which the Daleks planned to reside on when the reality bomb destroyed the universe. (TV: Journey's End)

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, which the Doctor thwarted. (TV: Doomsday) Time traveling 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. (TV: 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.

In 2009, the Daleks transported 27 planets into the Medusa Cascade from various times and places (mostly the present, but from other eras as well). The new Daleks then took control over the planets in the Cascade. In their attack on Earth, they took many humans aboard their ships, and wiped out any resistance that they met. (TV: 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, through Dalek Caan's manipulation of the timeline, Donna Noble shut down this device. The Meta-Crisis Tenth Doctor wiped out the Daleks and their fleet by targeting their Dalekanium with their own technology. (TV: Journey's End)

Legacy
The New Dalek Empire was obliterated during the destruction in the Medusa Cascade, except for three individuals which barely survived. In their damaged saucer, they located a Progenitor device containing pure Dalek DNA, and eventually initiated the New Dalek Paradigm. The first five Paradigm Daleks detected that their three predecessors were "unclean" (since they were created from Davros's cells, not pure Dalek DNA). When the Paradigm Daleks stated that they would kill them, the last three New Empire Daleks eagerly submitted. They were completely disintegrated, much to the surprise of the Eleventh Doctor, and the New Paradigm Daleks went on to establish an empire vastly larger than even the New Empire had been. (TV: Victory of the Daleks)

Rusty, a New Paradigm Dalek, observed visions of the New Dalek Empire's attack on the Valiant, and the Empire's destruction, when he saw into the mind of the Twelfth Doctor. In doing so, he felt the Doctor's hatred for the Daleks, and turned against his own kind, massacring the Dalek boarding party aboard the Aristotle. (TV: Into the Dalek)