I take it your are referring to Muslims. While it may be true that not all Muslims are extremists, the fact remains that the Koran and Islam do teach Jihad (holy war) against the infidels, and the extremists are the ones who are interpreting the Koran as it was meant to be. There are 164 verses in the Koran about Jihad, and the reward is Paradise.
[Sura 2.190] ...fight in the way of Allah with those who fight with you...
[Sura 2.191] And kill them wherever you find them, and drive them out from whence they drove you out, and persecution is severer than slaughter, and do not fight with them at the Sacred Mosque until they fight with you in it, but if they do fight you, then slay them; such is the recompense of the unbelievers [infidels].
[Sura 8.012.] Your Lord inspired the angels: “I am with you, so support those who believe. I will cast terror into the hearts of those who disbelieve. So strike above the necks, and strike off every fingertip of theirs.”
[Sura 8.013.] That is because they opposed Allah and His Messenger. Whoever opposes Allah and His Messenger—Allah is severe in retribution.
Islam claims to be the religion that supersedes Judaism and Christianity, and Muslims established a Caliphate in Europe about 500 years ago. They tried to convert Christians to Islam by the sword, or killed them. Today, ISIS and Turkey are trying to establish a worldwide Caliphate which will include all the atrocities we have heard and read about.