The ancient Berber script is probably based on or derived from the Punic script, with some influence from the South Arabian and North Arabian scripts. The earliest inscriptions for which the dates are known were inscribed sometime during the 2nd century BC, though the ancient Berber script may be six or seven hundred years older than that. The script was until at least the 3rd century AD, possibly later.
From the 12th century onwards, Berber languages were written with the Arabic abjad. There are also some Berber texts in the Hebrew abjad written by Berber Jews. A version of the Berber script, known as Neo-Tifinagh is still used to some extent in Morocco.
Information about the Ancient Berber script
Monde Berbere (Berber World) - information on the Berber people of Morrocco in Berber, French and English: http://www.mondeberbere.com
Amazigh World - information about the Berber language and people (in English, French and Berber): http://amazighworld.net/