As the story goes: in 1946 or 1947 (just a couple of years after the purported discovery of the Nag Hammadi library), a young Bedouin called Muhammad "the Wolf" searching for a lost goat threw a rock in a cave and, hearing an unexpected sound of breaking pottery, ventured inside and found an ancient set of scrolls wrapped in linen and concealed in jars. The Bedouin and his companions (part of a smuggling ring, as it turns out) brought the strange scrolls to Jerusalem where, through somewhat unclear events, some of them ended up in the hands of a Christian monk in Jerusalem. Some of these early Scrolls were transcribed and published by U.S. scholars working in Jerusalem, while the monk took some to the U.S. to try to sell them (they eventually were bought by Yigael Yadin and repatriated to Israel). Other scrolls soon turned up on the Jerusalem antiquities market and, in the later 1940s and early 1950s, excavations in the surrounding caves turned up thousands of additional fragments and evidence of a settled in this desert outpost. The story of Muhammad "the Wolf" was popularized early on by Edmund Wilson, who wrote a long "dispatch" for The New Yorker in 1955 (and later published a book).
How much of this initial "discovery" story is true? It's impossible to say. The earliest announcements claimed the first scrolls had turned up in a monastic library in Jerusalem decades earlier (this was later explained as either a misunderstanding or a deliberate deception on the part of the Christian monk who wanted to obscure the find site). A very few experts at the time, most prominently Jewish studies scholar Solomon Zeitlin, the editor of the U.S. Jewish Quarterly Review, disputed the antiquity of these scrolls altogether. But for the most part the "discovery" was hailed as a watershed in biblical discovery (particular as the first scrolls to be made public were texts from the Hebrew Bible).
After 1948 and the establishment of the State of Israel the political context of what were now known as "the Dead Sea Scrolls" was fractured and contentious. Some of those initial scrolls, supposedly found by Muhammad, ended up in the possession of scholars at the Hebrew University which, after 1948, was located in the Israel. The caves where further discoveries and excavations were undertaken were located in the possession of Jordan. For more than a decade, study of the Scrolls took place in separate worlds. The territories and Scrolls were nominally united by the Israeli acquisition of land after the 1967 war but the unpublished scrolls remained under the control of the École Biblique; the process for publishing these discoveries remained excruciatingly slow for the next several decades. Outsiders, and even some disaffected former scholars who had worked on the Scrolls, began criticizing the slow pace of publication; conspiracy theories spread that the Catholic École Biblique was suppressing Scrolls that might contain shocking new evidence about Christ or Christian origins.
In the early 1990s, a series of actions taken by scholars in the United States effectively broke the monopoly of the Israeli Department of Antiquities and the École Biblique and all of the texts discovered to that point were published. Most scrolls are now housed in a museum in Israel and are available to view online.
To date none of the Dead Sea Scrolls have said anything about Jesus or his movement: they seem to comprise the centuries-old library of sectarian Jewish group that had a settlement in the desert outside of Jerusalem. In addition to biblical books the Scrolls contain parabiblical literature, in Hebrew and Aramaic, rules for sectarian life, and anticipation of the coming war of the end times. This lack of explicit connection to earliest Christianity has not stopped both scholars and popular writers, since the 1960s, of positing a deep connection between the Dead Sea community and Christianity and of maintaining a hope (or fear) that some new "Dead Sea Scroll" might emerge that speaks directly to Christian origins. New scrolls (some forgeries, some possibly authentic) do continue to appear on the antiquities market and the State of Israel continues to sponsor archaeological searches in the area along the Dead Sea.
The timing of these "discoveries" has given them a complicated role in the U.S. biblical imaginary, linked to various hopes and fears, and conspiracies, about Zionism, the Jewishness of Jesus, and the middle eastern origins of the New Testament.
You'll find links below to novels that make significant use of the "Dead Sea Scrolls" in their plots.