Livy, born 53 BC, died AD 17, wrote a history of Rome in 142 books. (These books were shorter than what we generally think of as books. Think books of the Bible instead. Back then, the term referred to the amount of writing which fit into a scroll.)
Of those 142 books, 35 have survived to our day: books 1-10 and 21-45. But we know a lot about what was written in the other 107 books: there is an anonymous 4th-century abridgment of 140 of the 142 books (136 & 137 are missing) referred to as the periochae of Livy. Altogether the periochae are about as long as one of Livy's books. Another anonymous abridgment, of books 37-40 (still extant in the entire form) and 48-55 (lost) was found at Oxyrhynchus in Egypt, and published in volume IV of the Oxyrhynchus Papryri in 1904. In addition, Julius Obsequens, who probably lived in the 3rd century AD, compiled a book of prodigies, or, as we might say, of wonders -- droughts, storms, ecplipses, swarms of bees, unexplained things seen in the sky, etc -- taken from Livy's history.
Also, the works of history written by Aurelius Victor, Florus and Eutropius consist to a great degree of abridgments of Livy.
In addition, there are fragments of Livy: a 1000-word passage from book 91 found in a 5-th century palimpsest of a manuscript in the Vatican library in the 18th century; a piece of parchment containing a few words from book 11, written in the 5th century, found in the Fayum in Egypt in the 1980's.
Quintus Aurelius Symmachus, in a famous letter from AD 401, says that his household is busily editing the whole of Livy's work.
And then there are the fragments which are the subject of this post: quotes from or other references to the lost books of Livy in the works of other authors, from the 1st to the 6th century AD. I have been able to identify the following references. Perhaps there are more. Perhaps some of these are spurious. In addition to these, I have found numerous references to the lost books in scholia (notes written inn the margins of manuscripts), for which I have as yet been able to determine neither an author not a date.
Servius, in the commentary on Vergil he wrote in the 4th century, refers to Livy's books 12, 13, 16, 19, 94, 99, 116, and 6 times to book 136.
Priscian, a 6th-century grammarian, refers to books 14, 17, 56, 112 (twice), and to 113, 118 and 136.
Censorius, a 3rd-century grammarian, refers to books 19 and 49.
Plutarch, in works written in Greek which cover some of the same ground as Livy, refers to books 77, 98 (twice), 111 and 116.
Valerius Maximus refers to book 18.
Augustine of Hippo refers to books 77 and 78.
Frontinus (c30-104) in his book on military strategy, refers to books 91 and 97.
Bishop Agrocius of Sens (5th cent) refers to book 102.
Josephus refers to book 102 in Antiquities of the Jews.
Serenus Sammonicus (d 212), in his book Res reconditae, refers to book 103.
Tacitus refers to book 105.
Jordanus (active mid-6th century) refers to book 105.)
Orosius (375 -- after 418) refers twice to book 109.
Appian refers to book 114.
Jerome refers to book 114.
Seneca refers to book 116 and 3 times to book 136.
Pliny the Elder refers twice to book 136.
Pope Gelasius refers to book 136 in AD 496.
Nonius Marcellus, writing in the 4th or 5th century, refers twice to book 136.
Quintilian refers twice to book 136.
The number of late citations by authors with connections to Africa is striking. (Pope Gelasius, for example, was a Berber.)