Let's be honest, the prophets (Isaiah- Malachi) were written to a people group that isn't most of us (ancient Israel and Judah), in a time period and place that is no longer relevant to us, so why was it included in the Bible and why should we drudge through the monotony and redundancy that sums up the writings of the prophets?
I have a few thoughts as to why I think this section of Scripture is relevant for readers today, particularly if you identify with the Christian faith. As far as practical relevance is concerned I think it serves as a historical record of the fall of Israel, and the development of the new covenant. In order to understand much of what Jesus and his apostles teach it is imperative to understand the history that they come from; they all started as pious Jews after all. A major theme among the prophets is the promise of a messiah. This sets the stage for the cultural and religious atmosphere for when Jesus is preaching his message.
There is also a great deal to learn about the character of God. If you believe that God is unchanging, and you have a relationship with this God, then is it not worth understanding God in these books which proclaim destruction? One attribute of God that is displayed through the writings of the prophets that is clear to me is that if you enter into a covenant with the Living God then break it, expect him to still abide by the terms of the agreement. Nothing that was done to the Israelites/Judahites should come as a surprise. It was all spelled out in the terms of the covenant that was originally made between them and God (then reaffirmed in Deuteronomy). So, if there is anything for a modern reader to apply from the prophetic texts today, it is that God will uphold the terms of his agreements. Jesus is yet another fulfillment of God's promise to his people, as well as all peoples of the earth.
Reading through the prophets can be difficult at times, but there is great reward for the diligent reader. What do you think of the prophets? Are there areas you find of interest, or struggle to understand? Feel free to share your thoughts in the comments!