The bombs that exploded in the Brussels airport and at a central metro station on Tuesday morning, killing at least 30 people, came as only the latest in a string of terrorist outrages on a continent that is starting to see horrific violence as the new normal. Hours later the Islamic State claimed responsibility.

This carnage must be seen in context: The United States and its Western allies are hitting the Islamic State hard in its bases in Iraq and Syria. The jihadist group may finally be on the defensive. But meantime, it is lashing out, taking its fight — and its struggle for supremacy among jihadists — global. Europe has emerged as a key battleground.

Working with Western and Iraqi partners, American forces have pushed back the Islamic State. The group has lost an estimated 40 percent of its territory in Iraq and 20 percent in Syria from its peak in the summer of 2014. Major cities like Ramadi have been reclaimed, and Mosul, the Islamic State’s de facto capital in Iraq, may be next. American military officials say that the group has lost more than ten thousand fighters.

These losses hurt the Islamic State twice over. The control of territory and the establishment of a “caliphate” is one of the big differences between the Islamic State and jihadist organizations that have preceded it. Qaeda leaders have long opposed such a move, arguing that it is premature, even foolhardy. The Islamic State, however, has gained legitimacy and popularity among radical Muslims by creating a “state” where they can live under their interpretation of Islamic law. Losing territory is a blow to its ambitions and legitimacy.