Short answers, pulled from the story.
The Vatican Library was formally established on the 15th of June 1475 by Pope Sixtus IV through the papal bull Ad decorem militantis ecclesiae. The collection predates that official founding, tracing back to Pope Nicholas V, who began assembling manuscripts at the Vatican in 1451.
The Vatican Library holds 75,000 codices, more than 1.1 million printed books (including around 8,500 incunabula), and 330,000 Greek, Roman, and papal coins and medals. By 1992, the library had almost two million catalogued items in total.
The Codex Vaticanus Graecus 1209 is the most celebrated holding: the oldest known nearly complete manuscript of the Bible. The library also holds the sole surviving copy of the Hadith Bayad wa Riyad, an Arabic love story, and the original manuscript of the Secret History by Procopius, which was published in 1623 after being discovered in the collection.
The Vatican Library is open to anyone who can document their qualifications and research needs. Up to 200 scholars may use it at one time, and the library receives between 4,000 and 5,000 visitors per year, most of them academics doing post-graduate research.
In 1809, Napoleon Bonaparte had Pope Pius VII arrested and ordered the library's contents seized and removed to Paris. The collection was returned in 1817, three years after Napoleon's defeat and abdication.
On the 20th of March 2014, the Holy See announced an agreement with NTT Data Corporation to digitize approximately 3,000 manuscripts, with equipment and technicians valued at 18 million euros. The resulting high-definition images are available through DigiVatLib, the library's free digital access service, stored on a three petabyte server provided by EMC.