Return of the Exiles
Jews have lived in Iran since members of the exiled Ten Tribes ended up there as slaves and migrants. The Jews arrived in Iran in comfort after Persians conquered the Babylonians in Biblical times (see Daniel 5:30, 6:1). Not long after that, the miracle of Purim happened, featuring Esther and Mordechai.
Between then and the mid 20th-century, there were always individuals who made their way back to the Land of Israel, but never in large numbers. The founding of the State of Israel in 1948 changed that.
Of the approximately 145,000 Jews in Iran, it is estimated that around half, or 70,000 Iranian Jews immigrated to Israel between 1948 and 1978. Unlike other Muslim countries, Iran interestingly never expelled its Jews, like due to the because the Westernized and secular character of the Persian monarchy.
The Islamic Revolution in 1979 gave Iranian Jews more good economic and religious reasons to leave. During and after the Revolution, an additional 20,000 Iranian Jews moved to Israel. The Islamic Republic is virulently anti-Israel and bars Iranian Jews visiting or moving to Israel.
The number of Persian Jews currently living in Israel is believed to be around 225,000.