Asia

Central Asia
Central Asia had been influenced by Buddhism probably almost since the time of the Buddha. According to a legend preserved in Pali, the language of the Theravada canon, two merchant brothers from Bactria, named Tapassu and Bhallika, visited the Buddha and became his disciples. They then returned to Bactria and built temples to the Buddha (Foltz).
Central Asia long played the role of a meeting place between China, India and Persia. During the 2nd century BCE, the expansion of the Former Han to the west brought them into contact with the Hellenistic civilizations of Asia, especially the Greco-Bactrian Kingdoms. Thereafter, the expansion of Buddhism to the north led to the formation of Buddhist communities and even Buddhist kingdoms in the oases of Central Asia. Some Silk Road cities consisted almost entirely of Buddhist stupas and monasteries, and it seems that one of their main objectives was to welcome and service travelers between east and west.
The Theravada traditions first spread among the Turkic tribes before combining with the Mahayana forms during the 2nd and 3rd centuries BCE to cover modern-day Pakistan, Kashmir, Afghanistan, eastern and coastal Iran, Uzbekistan, Turkmenistan and Tajikistan. These were the ancient states of Gandhara, Bactria, Parthia and Sogdia from where it spread to China. Among the first of these Turkic tribes to adopt Buddhism was the Turki-Shahi who adopted Buddhism as early as the 3rd century BCE. It was not, however, the exclusive faith of this region. There were also Zoroastrians, Hindus, Nestorian Christians, Jews, Manichaeans, and followers of shamanism, Tengrism, and other indigenous, nonorganized systems of belief.
Various Nikaya schools persisted in Central Asia and China until around the 7th century CE. Mahayana started to become dominant during the period, but since the faith had not developed a Nikaya approach, Sarvastivadin and Dharmaguptakas remained the Vinayas of choice in Central Asian monasteries.
Various Buddhism kingdoms rose and prospered in both the Central Asian region and downwards into the Indian sub-continent such as Kushan Empire prior to the White Hun invasion in the 5th century where under the King Mihirkula they were heavily persecuted.
Buddhism in Central Asia started to decline with the expansion of Islam and the destruction of many stupas in war from the 7th century. The Muslims accorded them the status of dhimmis as "people of the Book", such as Christianity or Judaism and Al-Biruni wrote of Buddha as prophet "burxan".
Buddhism saw a surge during the reign of Mongols following the invasion of Genghis Khan and the establishment of the Il Khanate and the Chagatai Khanate who brought their Buddhist influence with them during the 13th century, however within a 100 years the Mongols who remained in that region would convert to Islam and spread Islam across all the regions across central Asia. Only the eastern Mongols and the Mongols of the Yuan dynasty would keep Vajrayana Buddhism.

Parthia
Buddhism expanded westward into Arsacid Parthia, at least to the area of Merv, in ancient Margiana, today's territory of Turkmenistan. Soviet archeological teams have excavated in Giaur Kala, near Merv, a Buddhist chapel, a gigantic Buddha statue, as well as a monastery.
Parthians were directly involved in the propagation of Buddhism: An Shigao (c. 148 CE), a Parthian prince, went to China, and is the first known translator of Buddhist scriptures into Chinese.

Tarim Basin
The eastern part of central Asia (Chinese Turkestan, Tarim Basin, Xinjiang) has revealed extremely rich Buddhist works of art (wall paintings and reliefs in numerous caves, portable paintings on canvas, sculpture, ritual objects), displaying multiple influences from Indian and Hellenistic cultures. Serindian art is highly reminiscent of the Gandharan style, and scriptures in the Gandhari script Kharosthi have been found.
Central Asians seem to have played a key role in the transmission of Buddhism to the East. The first translators of Buddhists scriptures into Chinese were either Parthian (Ch: Anxi) like An Shigao (c. 148 CE) or An Hsuan, Kushan of Yuezhi ethnicity like Lokaksema (c. 178 CE), Zhi Qian and Zhi Yao, or Sogdians (Ch: SuTe/粟特) like Kang Sengkai. Thirty-seven early translators of Buddhist texts are known, and the majority of them have been identified as Central Asians.
Central Asian and East Asian Buddhist monks appear to have maintained strong exchanges until around the 10th century, as shown by frescoes from the Tarim Basin.
These influences were rapidly absorbed however by the vigorous Chinese culture, and a strongly Chinese particularism develops from that point.