Because of the Crusades, the Christian as well as the Islamic world had 360 degrees changes and negative long-term effects. Before the crusades most of Christians were pacifists and regard Jesus Christ as the Prince of peace; but due to the Crusades, Christians' posture about violence totally changed. From their perspective violence could be justified if it was used just in wars to defend their church and God's mandates. Although at first, the Crusades were used in order for Christian pilgrimages to access the Holy city of Jerusalem, which was something good because the Muslims had taken control over the city and didn't let them in. Later on, the Crusaders lost their original path and promoted religious warfare for two and half centuries committing pillaging, murder among other atrocities not only against Muslims but also against any other vulnerable minorities.
Crusades also helped to elevate the authority of the papacy as the authoritative spiritual and temporal power in Europe before the emergence of the nation-states. Nowadays, because of the way Crusades develop most Muslims regard them as cruel and savage onslaughts by European Christians.
I'm pretty sure they are just known as the common law
