Final answer:
The Christian kingdoms of Europe primarily responded to Islam's expansion through military resistance, notably the Crusades, but also engaged in trade and political alliances with Islamic states when it was beneficial for both sides.
Step-by-step explanation:
The Christian kingdoms of Europe largely reacted to Islam's expansion by launching a series of military crusades against Islamic territories. This included efforts to take back control of Jerusalem and other Holy Land areas. Beyond these crusades, the complex dynamics of medieval power politics also led to European Christian kingdoms sometimes trading with and forming alliances with Islamic empires when it suited mutual benefits, or warring against each other irrespective of religious affiliations. Moreover, Christian conquests in the Iberian Peninsula ultimately pushed Islamic rule southward until the Reconquista was completed in 1492.
While the primary response was one of military resistance exemplified by the Crusades, there were also instances of peaceful interactions such as trade, as well as political and economic engagements between Christian and Islamic states. However, such moments of cooperation did not overshadow the overall conflict and competition that characterized the relationship between the Christian kingdoms and the Islamic caliphates during the medieval period.