One particular theory (or, if you're a wahabi, a criticism) of the origins of Sufism is that it was a reworking of the mystical pre-islamic beliefs of many areas of the Islamic world, but particularly Khorasan and Transoxania (i.e., modern day Iran and central Asia), as well as the beliefs of the Christian Monks and Hermits that inhabited the captured areas, and the employment of mystical elements of the Alid line, into a format more suitable to Sunni Scripturalist belief. Sufism as a written tradition that can be attached to Islamic belief can be tied to such figures as Junayn, a Baghdadi mystic of the 9th century, who in his writing gives as a clear view of the general format of Sufi belief-Faith is illogical, and God is better reached through mystical practices than the academic practices of the Islamic schools of law (Hadith) as represented by such figures as Ibn Hanbal, founder of the Hanbali school, or the philosophical inquiry of later scholars such as Ibn Sinna (Avicenna) and Ibn Rushd (Averroes). This general framework of belief would continue to play a major role in Islamic thought, but would have it's true cultural and political efflorescence in the 11th century, with the Turkish entry into Anatolia and the Levent. The Seljuk Turks, for example, under the Sultan Malik Shah, would attempt to legitimize their rule (having no direct connection to the prophet, obviously), by serving as 'defenders of the faith', gaining prestige by opposing the, Shi'ite, Fatimids and supporting the Sunni Abbasid Caliphs. Malik Shah, or rather, his vizier, Nizam al-Mulk, would be instrumental in the ideological reinforcement of Sunni Islam, and a large part of this would come from their employment of Sufism as a means of exerting populist control over the faith. A perfect example of the application of Sufist doctrine to the Sunni Orthodox tradition can be seen in the figure of al-Ghazali, a Sunni scripturalist by training who would in his writing attempt to reconcile the mysticism of the Sufi with the logic, ritual, and Koranic study of the Sunni legal scholar. Sufism would not only play a major part in the popular Islam that would convert millions of Christian and Jewish inhabitants of the empire, but it would also allow the formation of Sufic brotherhoods that were enormously politically influential throughout history, for example in the close connections between the Bektashi order in Anatolia and the Ottoman Janissaries, or in the Safaviyya order and the formation of the Safavid Persian Dynasty. Anyway, I'm by no means an expert in the field, but if you're interested in reading more about the historical implications of Sufism, you could check out Caroline Finkel's 'Osman's Dream', which is a really fantastic book centered on the Ottoman Empire that has a very interesting section on the influence of the Bektashi and Safaviyya orders, and the conflict that would arise between these groups and the Ottoman state. For a more modern analysis of Sufism, I've been advised Julia Howell's 'Sufism and the "Modern" in Islam.' Anyway, happy reading!

If you're interested in influential Sufi figures, you could look at Hassan al-Banna, founder of the Muslim Brotherhood. In much of his teaching (and by extension the practices of Muslim Brothers today) you find traces of Sufism, such as the use of wird, basically "prayer-recipes". An example of a wird is al-Ma'thurat. Another such Sufi practice, which is also found in al-Ma'thurat, is dhikr, meaning a repetition to reach a meditative state in which you will continue Qur'an recitation.

Al-Banna in turn was heavily influences by Mohamed 'Abduh, who was a student of al-Afghani. Many scholars today argue that 'Abduh was a much more important figure than the latter, as many of al-Afghanis teaching were seen as controversial, and disregarded.

Source (unfortunately in my native language Swedish):

Stenberg, Leif (2012) "Nedsändelserna, al-Ma'thurat: En handledning i konsten att vara en from muslim" in Islamologi: Studiet av en religion, Jonas Otterbäck & Leif Stenberg (eds.) Stockholm: Carlsson.

Perhaps there was no more influential figure in Islamic history after the Prophet and his Companions than Abu Hamid al-Ghazali. In addition to refuting and sidelining the Mu'tazila (an unorthodox philosophical group), he reconciled the orthodoxy of Islam with the spirituality of Sufism. His Ihya 'Ulum al-Din is almost universally accepted as a monumental work of Sufism/self purification in accordance with Islamic law.