By far the greatest living expert on the Vicksburg Campaign is Edwin C. Bearss, chief historian of the National Park Service and longtime historian at the Vicksburg National Military Park. His mammoth three-volume study The Campaign for Vicksburg (Dayton, Ohio, 1985-1986) is by far the most detailed account of the battle and siege. These volumes, however, study only Grant's several campaigns against the city and do not cover the interesting 1862 naval expeditions. It should also be noted that Bearss' style is a bit dry and analytical.
Bearss is also the author of several other monographs dealing with the campaign. His Decision in Mississippi (Jackson, 1962) covers all the wartime activity in the state, including the battles of Iuka and Corinth and other actions not covered in The Campaign for Vicksburg. Bearss was responsible for the salvaging of the USS Cairo, and wrote Hardluck Ironclad, The Sinking and Salvage of the Cairo in 1966. Yet another campaign study by him is The Battle of Jackson, the Siege of Jackson, and Three Other Post-Vicksburg Actions (Baltimore, 1981).
There are numerous recent narrative accounts of the Vicksburg campaign that give a good overview supplemented with anecdotes and human interest stories. The best of these are: The Final Fortress, The Campaign for Vicksburg, 1862-1863, by Samuel Carter III (New York, 1980); The Web of Victory, Grant at Vicksburg, by Earl S. Miers (New York, 1955); Vicksburg: 47 Days of Siege, by A.A. Hoehling (Englewood Cliffs, 1969); and Grant Moves South by Bruce Catton (New York, 1960).