Short answers, pulled from the story.
Ctesiphon was located on the eastern bank of the Tigris River, approximately 35 kilometres southeast of modern Baghdad in present-day Iraq. The site corresponds to the modern town of Al-Mada'in, and the most visible remaining structure, the Taq Kasra, stands in the Iraqi town of Salman Pak.
Ctesiphon served as a royal capital of Iranian empires for over eight hundred years, spanning both the Parthian and Sasanian periods. It became the Sasanian administrative capital in 226 and held that role until the Arab conquest in 637.
Roman forces captured Ctesiphon four or five times in its history. Three of those captures occurred in the 2nd century alone: the emperor Trajan took it in 116, Avidius Cassius seized it in 164, and Septimius Severus sacked it in 197, carrying off thousands of inhabitants whom he sold into slavery.
The Taq Kasra, also called the Arch of Ctesiphon, is the most conspicuous structure remaining from the ancient city. It was once part of the royal palace in Ctesiphon's southern district and is estimated to date from between the 3rd and 6th centuries AD. In 2013, the Iraqi government contracted to restore it as a tourist attraction.
After the Arab occupation in 637, the city fell into rapid decline as political and economic power shifted elsewhere. The founding of the Abbasid capital at Baghdad in the 760s accelerated the process. Caliph Al-Mansur took building materials from Ctesiphon's ruins for Baghdad's construction, and the city was largely depopulated by the end of the 8th century.
The major excavations were conducted in the early 20th century. Oscar Reuther led a German Oriental Society expedition there in 1928-29. A joint German-American expedition involving the German State Museums and the Metropolitan Museum of Art followed in 1931-32, directed by Ernst Kühnel. An Italian team from the University of Turin, led by Antonio Invernizzi, worked at the site in the late 1960s and early 1970s.