The Jewish question was the name given to a wide-ranging debate(s) pertaining to the appropriate status and treatment of Jews in society.
Such a debate has existed at least since Christianity became the majority and state religion of the Roman Empire. Unlike other non-Christian religions and perceived Christian heresies, Judaism was given a special exemption and allowed to continue to exist instead of being forbidden like all other non-state religions. This created a number of questions regarding the relations between Judaism and the state religion and between Jews and non-Jews.
However, various questions existed already before this, such as how to deal with the refusal of the monotheistic Jews to acknowledge as gods the Greek kings and Roman emperors proclaimed as such.
Less politically correct aspects of these debate(s) include Jewish influence in a society, how it was acquired and used, and perceived resource competition between Jews and non-Jews. See also Jewish group evolutionary strategy.
In a number of cases the co-existence ended (at least for a time) with Jewish expulsions (the most recent being the large scale expulsion/migration of Jews from most Muslim countries).
However, the phrase "the Jewish question" often refers more narrowly only to the debate that began with the Age of Enlightenment and the French Revolution and the consequent demands for equal rights and equal treatments of all groups (including Jews) in a society. At the same time, another trend was increased nationalism and demands for greater national unity which opposed continued Jewish separateness.
One argued solution was Jewish assimilation.
Regarding the phrase "The Final Solution of the Jewish Question",see Meanings and translations of German words and Holocaust revisionism: The "Final Solution of the Jewish Question".