Since there are so many of these darn things the review shall be divided into three sections. First, a brief description of the Loeb series of books and their advantages/disadvantages. Second shall be my thoughts on the author himself, his accuracy, as well as his style and the style of his translator. This is of course only my opinion and should be treated as such. The final part shall review what this particular book actually covers.
The Loeb series date back to the turn of the last century. They are designed for people with at least some knowledge of Greek or Latin. They are a sort of compromise between a straight English translation and an annotated copy of the original text. On the left page is printed the text in Greek or Latin depending on the language of the writer and on the right side is the text in English. For somebody who knows even a little Greek or Latin these texts are invaluable. You can try to read the text in the original language knowing that you can correct yourself by looking on the next page or you can read the text in translation and check the translation with the original for more detail. While some of the translations are excellent mostly they are merely serviceable since they are designed more as an aid to translation rather than a translation in themselves. Most of them follow the Greek or Latin very closely. These books are also very small, maybe just over a quarter the size of your average hardcover book. This means that you'll need to buy more than just one book to read a complete work. They are also somewhat pricey considering their size. The Loeb Collection is very large but most of the more famous works can be found in better (and cheaper) translations elsewhere. If you want to read a rarer book or read one in the original language then you can't do better than the Loeb Editions.
Diodorus' Library of History takes up twelve volumes in the Loeb series. Diodorus was a Sicilian who wrote a universal history sometime in the first century BC. His work covers both Roman and Greek history and is useful for providing a general Mediterranean view of classical history. Diodorus' work is generally derided for its use of myth and for shamelessly reproducing exactly what was printed in his sources. The first part however is where we get much of our information about Greek myths while the second is made more bearable by the fact that he is exceptionally scrupulous about recording what those sources are. Since most of these sources have been lost over time Diodorus' account is invaluable in piecing together what they said. This isn't to completely dismiss his flaws since he quite often misinterprets his sources or muddles the timeline. But while there are better sources for much of his material covering the Persian and Peloponnesian Wars, for the section covering the Hellenistic period Diodorus is our primary source. Unfortunately even his work is incomplete. Out of an original 40 books only books 1-5 and 11-20 survive intact. The rest exist only in fragments. Diodorus covers a lot of ground from the period before the Trojan War to Julius Caesar's Gallic campaigns. For that reason his book is divided into three sections. The first section (books 1-6) cover the carious myths in a historical way and are divided geographically. The second section (7-17) offers a history of the world from the Trojan War to the death of Alexander the Great. The third section (18-40) covers world history from the early Hellenistic kingdoms through to the campaign of Julius Caesar. Regrettably, most of that last section is missing. The division of the volumes in the Loeb series is rather atrocious. Why they split books in two I'll never know. While many have criticized Diodorus for being inaccurate, nobody has accused him of being dull. He's worth a read even if he's often of little use.
At this point we're basically reliant almost entirely on Diodorus for the narrative of this period. There's also Justin, but his epitome of Pompeius Trogus' work is brief, innacurate, and often quite odd in its selection of what's important. While the various kingdoms are somewhat more settled the kings are still jostling for the top spot. If you're confused about what's going on there's an excellent book by Peter Green called Alexander to Actium that outlines the entire Hellenistic period in detail. This is the last book of Diodorus to survive intact unfortunately. The rest of his work exists only in fragments.