The group that has developed into ISIS originated in the early 2000s under Abu Musab al-Zarqawi (a Jordanian). al-Zarqawi's organization, Jama’at al-Tawhid wa’al-Jihad, was a Salafi militant organization that eventually pledged allegiance to Al Qaeda and came to be know as Al Qaeda in Iraq. The group rose to prominence in the chaos that followed the American invasion of Iraq and group was marked by its extremely violent and destructive tactics. The group's leader, al-Zarqawi, was killed in an American airstrike in June of 2006. His successor, Abu Ayub al-Masri (an Egyptian), changed the name of the organization to the Islamic State of Iraq and named Abu Umar al-Baghdadi (an Iraqi) as its leader.
With the Anbar Awakening (local Sunni resistance to the group) and the US troop surge in 2007, the group struggled and began to decline. By 2010, 34 of the groups 42 highest leaders had been killed, with al-Masi and Abu Umar al-Baghdadi being killed in April of 2010. Abu Bakr al-Baghdadi became the leader of an organization that was a shell of its former self. However, due to US troop withdrawal in late 2011, the sectarian policies of the Maliki government, and the instability in neighboring Syria, the group was able to return to prominence. Al-Baghdadi exploited these events and changed his organizations name to Islamic State of Iraq and Syria in April 2013. Over the next year and a half the group conquered large portions of Iraq and Syria including the cities of Fallujah, Ramadi, Mosul, and ar-Raqqa. In June of 2014, ISIS declared itself a caliphate with al-Baghdadi as the Caliph.
ISIS follows an extremely stringent interpretation of Islam (an interpretation many consider outside the bounds of Islam) and the group is hostile to essentially every other entity which does not ascribe to this same interpretation. ISIS is known for its brutality, indiscriminate killing of civilians, savvy use of media, and its political ambitions. Unlike earlier jihadist groups like al Qaeda, ISIS has established a state as part of its drive to create a global caliphate in which it can impose its austere and brutal vision upon the world. The group, especially in recent years, has organized and/or inspired a variety of terrorist attacks throughout the world. Although initially triumphant, ISIS has gradually lost territory and soldiers in recent years.
The aforementioned information is partially drawn from the many reports and resources cited below (in particular Stanford's excellent Mapping Militants Project). See those resources for more detailed information. See the tab titled "News" for up-to-date information on the present situation.