What does an Old Testament book like Deuteronomy have to do with modern Christians? Simply this: We worship the same, unchanging God who entered into covenant relationship with Israel!
In Deuteronomy 1:1-8 we read the introduction to this book which calls Israel to loyal love expressed in obedience. Moses, the mediator of the covenant, speaks God's words and explains them to a new generation. In doing so, the very format of the book, which imitates ancient treaties, declares that God is the King of Israel. He is the one who disciplines and who provides. He is the one who saves and makes a people for himself. With the reminder of the 40 years of wandering in place of an 11 day journey, Israel is exhorted to give loyal obedience to their king.
As people who have confessed Jesus as Lord, we have entered into covenant relationship with the same God. This God remains the great king who meets all our needs and who continues to discipline his people for their good. Our challenge is the same as Israel's: