The Deuteronomistic History is a contemporary theory derived by Martin Noth arguing that the books of the Former Prophets of the Hebrew canon, Deuteronomy, Joshua, Judges, Samuel, and Kings, all came from one literary work. Prior to Noth's theory, scholars believed that these books were a collection of works that had been edited to reflect primarily on Deuteronomy; however, later, Noth built on several of these older theories, noting the "similarities in language, style, and content" in all five books, and proposed his theory that they were at once all one unified work written during the period when the Israelites had been exiled from Israel and brought to Babylon (Oxford Bibliographies, "Deuteronomistic History").
The Book of Deuteronomy is understood to be a covenant between Israel and Yahweh; Yahweh has chosen the Israelis to be his people, and in turn, the Israelites must follow Yahweh's laws, as set forth in Deuteronomy. In fact, the name Deuteronomy was derived from a mistranslation in the Septuagint, meaning the Greek translation of the Old Testament, of a phrase found in Deuteronomy 17:18; the phrase was translated to mean "repetition of the law," but the actual Hebrew means "copy of this law" ("Deuteronomy: Introduction from the NIV Study Bible"). All in all, the Book of Deuteronomy was named to reflect Yahweh's laws as a part of the covenant.
What's also important is the laws make it very clear that, if the Israelites fail to follow the laws, then they will lose Yahweh's protection and the promised land he has given them, Israel. Noth saw the Deuteronomistic History as an account of all of the Israelites successes and failures to uphold the laws and the destruction that was a consequence of their failures, such as the Assyrians' conquest of Israel in 721 BCE and the Babylonians' conquest of Judah in 586 BCE. Hence, the main theme within the Deuteronomistic History is the successes and failures to uphold the laws and the ensuing consequences ("Deuteronomist"). This theme is manifested in the Book of Joshua, which narrates the Israelites' conquest of Canaan, the establishment of Canaan as the promised land of Israel, and the division of the land among the tribes of Israel. The theme is further manifested in the Book of Judges, which has its own cyclical theme: "the people are unfaithful to Yahweh and he therefore delivers them into the hands of their enemies; the people repent and entreat Yahweh for mercy, which he sends in the form of a leader of champion (a 'judge'); the judge delivers the Israelites from oppression and they prosper, but soon they fall again into unfaithfulness"--the cycle continues from there ("Book of Judges"). The cycle of rebelliousness, repentance, and Yahweh's deliverance can be further seen in the Israelites demand for a king in the books of Samuel and the books of Kings.