The Latin name Libya referred to the region west of the Nile Valley, generally corresponding to modern Northwest Africa. Climate changes affected the locations of the settlements.
More narrowly, Libya could also refer to the country immediately west of Egypt, viz. Marmarica

Marmarica

Marmarica in ancient geography referred to the part of the North African coast between Cyrenaica and Aegyptus.It corresponds to what is now the border region between Libya and Egypt, including the towns of Bomba , Timimi , Tobruk , Acroma , Bardiya, As-Salum, Sidi Barrani .It...

 (Libya Inferior} and Cyrenaica

Cyrenaica

Cyrenaica is the eastern coastal region of Libya.Also known as Pentapolis in antiquity, it was part of the Creta et Cyrenaica province during the Roman period, later divided in Libia Pentapolis and Libia Sicca...

 (Libya Superior). The Libyan Sea

Libyan Sea

The Libyan Sea is the portion of the Mediterranean Sea, north of the African coast of ancient Libya, i.e. Cyrenaica and Marmarica...

 or Mare Libycum was the part of the Mediterranean south of Crete

Crete

Crete is the largest and most populous of the Greek islands, the fifth largest island in the Mediterranean Sea, and one of the thirteen administrative regions of Greece. It forms a significant part of the economy and cultural heritage of Greece while retaining its own local cultural traits...

, between Cyrene

Cyrene, Libya

Cyrene was an ancient Greek colony and then a Roman city in present-day Shahhat, Libya, the oldest and most important of the five Greek cities in the region. It gave eastern Libya the classical name Cyrenaica that it has retained to modern times.Cyrene lies in a lush valley in the Jebel Akhdar...

 and Alexandria

Alexandria

Alexandria is the second-largest city of Egypt, with a population of 4.1 million, extending about along the coast of the Mediterranean Sea in the north central part of the country; it is also the largest city lying directly on the Mediterranean coast. It is Egypt's largest seaport, serving...

.

In the Greek period

Hellenistic period

The Hellenistic period or Hellenistic era describes the time which followed the conquests of Alexander the Great. It was so named by the historian J. G. Droysen. During this time, Greek cultural influence and power was at its zenith in Europe and Asia...

 the Berbers

Berber people

Berbers are the indigenous peoples of North Africa west of the Nile Valley. They are continuously distributed from the Atlantic to the Siwa oasis, in Egypt, and from the Mediterranean to the Niger River. Historically they spoke the Berber language or varieties of it, which together form a branch...

 were known as Libyans, a Greek term for the inhabitants of northeast Africa.