The phrase, known as takbir in Arabic, is expressive of a range of moods and occasions in the Islamic world, from displays of approval and happiness to entreaties or spiritual and at times propagandistic cheerleading during political rallies.
The phrase has been tainted by its usage, or rather misuse, by Islamist extremists, salafists and terrorists, including the 9/11 terrorists, several of whom carried copies of a handwritten letters exhorting them to "strike like champions who do not want to go back to this world. Shout, 'Allahu Akbar,' because this strikes fear in the hearts of the non-believers."
The phrase was also used with political undertones in 1978 and 1979, during the Iranian revolution, as Iranians took to their roofs and shouted "Allahu Akbar" in defiance of the shah's regime. Iranians returned to the ritual in the aftermath of the fraudulent presidential election of June 2009.