Islamists have produced tectonic political shake-ups across the Middle East, with a rippling effect worldwide. Islamists now take many forms, from moderates in Tunisia to militants in the Islamic State, also known as ISIS.

Together, the disparate factions have arguably altered the Middle East more than any trend since the modern states gained independence over the past century. They have redefined politics and even borders.

The turmoil and transformation have in turn redefined security challenges for the outside world too. In early 2015, Americans overwhelmingly—by 70 percent—identified the Islamic State as the main threat to the United States, according to a poll by the University of Maryland. The next two top threats—the Palestinian-Israeli conflict (13 percent) and Iran (12 percent)—also involved Islamist movements.

Islamism is now one of the most powerful forces of the 21st century.

By 2015, Islamists generally fell into two broad camps: Political parties vying for position within systems. And extremists using violence or waging war to change the system from outside. Some factions have tried to be both. But by 2015, political groups and extremist militias have also become rivals for influence, and sometimes even enemies....