Elfen Lied takes place in Kamakura, Japan, focusing on a new strain of the human race, Diclonius, similar to human beings with invisible arms called vectors but different at the genetic level and notable due to physical abnormalities, particularly a pair of short horn-like protrusions. One such Diclonius, Lucy, is the main character of the series: Initially held in a facility built for experimentation, located off the coast of Kamakura, she manages to escape and wreak havoc, but is injured in the process, an event which causes her to develop a secondary, childlike personality known as Nyu.
Lucy is found by two locals, Kohta, who studies at the local university, and his cousin Yuka. They take her in, and become involved with the numerous, often brutal, attempts to recapture her by a Special Assault Team and a number of other Diclonius, who shift frequently from oblivious to murderous.
Much of the plot of Elfen Lied revolves around the Diclonii species, which strongly resemble humans; the only obvious difference are the two horn-like protrusions extending from the temporal and parietal regions of the skull.
Diclonii powers involve the use 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 Diclonii usually kill their victims. Vectors usually have a limited range of a few meters, but the length varies among each Diclonius. Diclonii also demonstrate the ability to sense one another.
A key point of debate 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. It is disputed and contradicted during the series as to how Diclonii develop their violent behavior, whether it is part of their genetic DNA or whether it stems from abuse by humans.
If a Diclonius vector penetrates or even so much as touches a human male body, the "vector virus" is transferred to the human, causing their children to be born as Diclonii (when born from humans they are called "Silpelits"). An incident involving the escape of a child Diclonius during Kurama's early years where the Diclonius' vectors penetrated him without causing him pain, resulted in Mariko being born a Diclonius and Kurama taking precautions against a recurrence by urging Bando to be sterilized. All Diclonii (Silpelits) born from human parents are sterile and female. There is only one Diclonius that is actually capable of reproducing: Lucy, the "queen".