The Arabs complete their conquest of Persia in 651. Umayyad, Abbasid.
Abbasid power there is lost, except in name, to local kingdoms, some of Persian, some of non-Persian origin. Persianisation a reaction to Arabisation. “Persianate” rulers may or may not have been ethnically Persian.
Samarkand and later Bukhara played a role in a revival of Persian civilisation under the native Persian Samanid dynasty (Sunni, ruled Persia 819-999). The Samanids sponsored the first complete translation of the Quran into Persian.
Mongol invasion. The Mongol House of Hulagu sets up the Ilkhanate. Tabriz is one of its capitals.
Ilkhans are followed by the Turco-Mongol Timurids from Transoxiana (Tamerlane). Capital Samarkand, now in Uzbekistan. (It is a Timurid prince, Babur, who, pursued by a west-Siberian section of the Golden Horde, the Uzbeks, founds the Mughal dynasty in India.)
Then a Persian renaissance (though Shah Ismail I spoke a Turkish language). The Ilkhans and Timurids had been Sunni. The Safavis are Twelver Shiite.
For four years (1511-14) the founder of the Safavi Empire, Shah Ismaʿil, threatened the Ottoman Empire with a repetition of the disaster that had been inflicted on it by Timur in 1402.
In 1598, the fifth Safavi, Shah Abbas I, moves his capital from Qazvin to Isfahan.
Afsharid, Zand, Qajar, Pahlavi dynasties follow. Allegiance to the Shia continues, but the Afshar make compromises with Sunni Islam.
The Afshar capital is Mashhad, Zand capitals Shiraz and Tehran. Tehran becomes sole capital in 1796 under Mohammad Khan Qajar. Persia is bled dry by Britain and Russia, but not officially colonised.
Then the revolution, violently Islamic: but Islam has never owned the whole of the Persian soul. Persia is a continuum under successive waves of Greek, Buddhist, Arab, Islamic (Arab and Islamic are not always the same thing), Turkic, Mongol and western culture.
Persia was also connected with China via the Silk Road. The Parthian and Sasanian empires had been in touch with the Han and Tang dynasties.
Mankind and Mother Earth, A Narrative History of the World, OUP, 1976, posthumous