When physical, the Scourge resembled gigantic black mantis-like insects. They acquired this form by mutating human bodies. Upon invading a host body and taking over, the "shadow" of the Scourge would appear on the hand of the host in the shape of a burned pentagram. This would allow the Scourge to invade the host's mind. The Scourge were physically stronger than humans. The Scourge were also a hive mind, meaning that if one of them was trapped between dimensions, they all were. (AUDIO: The Shadow of the Scourge)
The Scourge's voice inspired religious awe in humans, causing them to feel guilt and obey their commands. They had complete control over the human nervous system, allowing them to force humans into autoasphyxiation, pushing past the genetic failsafe against self-destruction. When at full power, they could traverse all of time and space instantaneously and bend time and space to connect points. In order for the Scourge to invade a universe, they would need a sacrifice and would also need huge amounts of fear and despair at the moment they materialised. (AUDIO: The Shadow of the Scourge)
While they seemed capable of awesome powers without technology, the Scourge made use of a time travel experiments to enter N-Space. They also utilised bio-dimensional implants, which they used on their humans to stretch them across dimensions and prolong their mutation for centuries. (AUDIO: The Shadow of the Scourge)
The Scourge were said to be a part of humanity ever since the first mammal became aware of itself and felt guilty for it. They lived in another plane of existence which had geometry reminiscent of Hell, giving the universe its name. They were also said to exist within all humans as their despair.
The Scourge believed the multiverse was organised so that humans would be their food. They had always been in contact with the humans (specifically psychics) who felt despair, depression, and fear on the astral plane. They referred to themselves as the manifestation of fear.
Finding the right point where they could invade the universe, they discovered the Seventh Doctor while he dreamed on the astral plane and he offered them the chance to invade Earth and the cosmos. They met him in 2003 at the Pinehill Crest Hotel and took the building into a fractional dimension, halfway between N-Space and Hell. The Scourge Leader met with the Doctor who, on behalf of Gallifrey, welcomed the Scourge and made up Earth's surrender papers for the Scourge to see. Focusing, the Leader, Demi-Leader, and Bridgehead tried to bring the others to invade, but the Doctor, going back and forth, became one with them when they betrayed him. He helped the Bridgehead and Demi-Leader to de-mutate, but was forced to spread the Leader across the dimensions for millennia. (AUDIO: The Shadow of the Scourge)