Much of the plot of Elfen Lied revolves around a species known as Diclonius which, as explained in the original manga version, are an evolutionary development from humans. Their bodies are very similar to humans', the only obvious difference being the two horn-like temporal protrusions which are said to relate to their telekinetic powers. In the manga, it is mentioned that Diclonius would fall into a coma if they lose one of their horns and would never return from their lethargic state if they lose both horns. However, Lucy manages to recover from this twice. In the anime, Lucy went into shock from losing one of her horns, and was temporarily rendered catatonic for a very brief period before recovering in time to save Nana.
Their powers involve the usage of invisible arms, known as "vectors" that can grasp and impact things as if they are solid, but also become insubstantial and pass through objects. They can slice objects as well, which is how Diclonius kill their victims. Vectors usually have a limited range of a few meters, but the length varies between Diclonius; Lucy's vectors are able to extend to 2 meters; Nana's can reach 5 meters , and Mariko's are the longest, with a range of 11 meters. Diclonius also have the ability to detect the location of others of their kind, such as when Kurama releases Nana from the offshore laboratory to search for and retrieve Lucy. However, when Lucy reverts to her "Nyu" state, Nana is unable to sense her; in the manga, Nana is also unable to sense Mariko when she is injured and reverts to a personality similar to Nyu.
A key dispute throughout the series is the Diclonius' propensity towards violence. Many have a vendetta against humans, and have ambitions to wipe out the human race and populate the world with their own species. If a Diclonius vector penetrates a human body, the "vector virus" is transferred to the human, causing their children to be born as Diclonius. An incident involving the escape of a child Diclonius during Kurama's early years where the Diclonius' vectors penetrated him resulted in Mariko being born a Diclonius, and Kurama takes precautions against a recurrence by attempting to sterilize Bando.
According to the manga, all Diclonius ("Silpelits") born from human parents are sterile and female (there were a few in the anime that were male), resulting in a structure resembling a beehive. There is only one Diclonius that is actually capable of reproducing: Lucy, the "queen".
It is disputed and contradicted during the series as to how Diclonius develop their violent behavior, whether it is part of their personality or whether it stems from abuse by humans, and both conclusions are supported by significant evidence. Kurama explains to Bandou that Diclonius are born with the intention of populating the world, and Lucy has implied to be directed by Diclonius instincts when she kills humans as a child. In the anime's final episode Lucy tells Kohta that "I was born to destroy humans." However, it is also shown that the Diclonius have usually been subjected to some type of severe psychological trauma; for example, Lucy was tormented by her human peers and witnessed the killing of her pet as a child, while Mariko was raised in neglect since her birth. They could therefore have developed their homicidal tendencies from abuse. Further supporting this view is the evidence of Nana's character. Unlike other Diclonius, Nana is good-natured and refuses to kill humans in order to please Kurama. Kurama implies Nana's nature is a direct result of his caring for her and treating her as a daughter while she endured horrific experiments at the Diclonius research facility.
Nevertheless, the researchers at the experimental facility believe the Diclonius to be nothing less than an existential threat. The Diclonius there are kept in isolation, where they are heavily restrained to the point of being unable to move and fed through tubes. Lucy mentions the danger to the human race to Kohta in the final episode of the anime: "Given just five years, I can ensure that there are more babies of our kind born in the world than there are normal humans."