I had no idea that Belisarius is revered by military historians. He was clearly important, but his fellow generals Narses and John Troglita were in my opinion just as skilled and certainly more important in securing the long-term stability of the western territories Belisarius reconquered (kind of, I don't think we can give the credit for winning Italy to Belisarius). I think most of Belisarius' reputation comes from the fact that his client, Procopius, wrote the most extensive secular history of the sixth century, which glorified Belisarius' earlier victories and minimised his defeats. It gets more complicated for the events of the 540s and 550s, when Procopius became disillusioned with Belisarius, but his later career isn't so well-studied and isn't nearly as prestigious as his earlier career anyway.

Belisarius' first victory was against the Persians at Dara in 530, but in 531 he led his army to a major defeat at Callinicum. Interestingly, Procopius blamed the defeat on the leader of the Arab auxillaries, Al-Harith, whilst another contemporary source writing in Constantinople, John Malalas, blamed Belisarius' incompetence. As Al-Harith's military skills are well-attested to, I see no reason why we should only believe Procopius' account - Belisarius was a good general, but not an undefeated one or one without his critics. Belisarius was recalled after this defeat and was caught up in the Nika Riots, where he was involved in the suppression of the rioters (along with other generals like Mundus and Narses, but again Belisarius was portrayed by Procopius as the most prominent figure), hardly something only a military genius could do.

Belisarius was then sent to Africa in 533 and quickly defeated the Vandals under Gelimer. This was indeed impressive, but the Vandal state was clearly ailing by this point, as Gelimer was an usurper and was facing pro-Byzantine rebels already in Libya. Still, contemporaries clearly thought that Belisarius played a major role in winning the war (he was rewarded a triumph after all), so this is probably the most clear-cut case of Belisarius being a military genius, in the short-term at least. Within a year, local Berbers rebelled and mutinies were common in the next decade; peace would not be restored until 548 at least and even then the country was supposedly devastated, so perhaps Belisarius' ability extended only to the tactical level? (Though of course we can also blame this on the corruption and incompetence of the Byzantine administration, so who knows!)

In 535 Belisarius invaded Italy and scored several quick victories, even securing Ravenna by 540, but Belisarius did not manage to inflict a crushing defeat on the Goths (the war only ended in 554). It is even possible that Belisarius' treacherous seizure of Ravenna actually motivated Gothic nobles to fight on rather than to make peace. In any case Belisarius was recalled at this point and sent to the east, as the Persians once again invaded Byzantine territories, but 541 did not see any major military successes - a campaign to Nisibis stalled and Belisarius led his army back to Dara, his main military base. Between 544 and 548 Belisarius was back in Italy, but he was now contending with a charismatic Gothic king called Totila; there would no longer be any easy victories for Belisarius, though another interpretation might be that he simply wasn't given enough resources to fight the war properly. The war was instead won by the eunuch Narses, who led a powerful well-funded army into Italy in 551.

Belisarius would not return to prominence until 559, when he raised a temporary force to defend Constantinople against Kutrigur raiders threatening the city - Belisarius by this point had been implicated in several conspiracies against Justinian and had retired from the military. This was a great victory for the Byzantines, but it is also symptomatic of the crisis facing the government in the late 550s, as their military situation was so precarious to the extent that they had no regular forces or generals available to defend Constantinople, having instead to rely on a retired general and volunteers.

From my perspective, Belisarius was certainly not anything like Alexander the Great, even though he did win several major battles. At a strategic level, he was not able to secure the loyalties of the locals or win miraculous victories when he did not have a material/political advantage. He also allegedly had a weak personality, being rather naive and trusting of his adulterous wife, if we believe the scandalous tales spread by Procopius in his Secret History. Unfortunately, Procopius is our main source for this period, so the image we get is rather schizophrenic, that of a young and successful general plagued by a whole host of personal issues. In reality, Belisarius was probably much more mundane, which for me makes him all the more interesting to study.

I think these answers are a bit unfair to Belisarius, who I believe deserves his reputation. I would rank his defense of Rome from 537-538 with the defense of Leningrad in WWII, Constantinople in 674-678 and 717-718, and Vienna in 1683 as one of the more astonishing defensive campaigns.

Belisarius made a career out of winning battles while outnumbered, often far from home, with almost completely useless infantry. Plagued by typical Byzantine manpower difficulties, particularly before the themata system, he relied on tactics more than almost any general in history, a rival to Frederick the Great, Jan Zizka, and Subotai in my view.

One example is the Battle of Dara against Sassanid Persia in 530. Unlike Alexander, whose sarissa phalanx gave him a huge force multiplier against lightly armored Persian infantry in particular, by Belisarius's time Roman infantry had devolved to conscripts with low morale, training, and poor armor and weaponry. This put him at a terrible disadvantage vs. Persian Immortals. The one saving grace was the famous Byzantine kataphractoi, heavily armored men and horses with barding armor, capable of fighting with both spear and bow. The problem is that Persians had been employing similar cavalry for a millennium, and matched the cataphracts in numbers. Belisarius set his infantry to practice archery and build breastworks. When the Persians initiated combat, the wind was at the Byzantines' backs, so the Sassanians withdrew. They then attacked the Roman left flank and drove them back, but Belisarius had been keeping a group of Hunnish cavalry hidden behind a hill, which he sent out as the left flank doubled back and drove off the Persians. The Immortals then pushed back the Roman right, and another detachment of Hunnish cavalry attacked again, allowing the right to double back and drive off the advancing Immortals. The main Persian line was now vulnerable on its flanks, which were attacked by cataphracts and Hunnish horsemen as the infantry advanced and shot arrows with the wind at their backs while staying out of range of Persian archers. The Persians were shattered and routed by numerically inferior and less trained forces in a pattern Belisarius would use later. Ltc. Robert Leonhard has a nice little essay on Belisarius's use of "small force" at www.jhuapl.edu/ourwork/nsa/papers/SmallForceTheory.pdf

The Vandals in North Africa were indeed politically divided and in tumult, but Belisarius knew how to take advantage by dividing and conquering. He persuaded Godas, the governor of Sardinia (part of the Vandal domain) to rebel, causing Gelimer to march forces to prepare to put down the rebellion. Belisarius then landed, unopposed, in Gelimer's rear. He conducted a lightning march, raising sympathetic forces along the way, and smashed the Vandal forces at Ad Decimum. Gelimer raised a larger army at Tricamarum, but Belisarius recognized it as the hastily assembled mob it was and his cataphracts routed it easily. This campaign shows that Belisarius knew when to strike quickly, to take advantage of the political situation after the coup against Hilderic.

I've probably written too much, though I could go on forever. Count Belisarius by Robert Graves (I, Claudius and Claudius the God) is a fun book, if not completely historically accurate, about Belisarius's life. In the end, Belisarius and Justinian's relationship was something like Flavius Aetius and Valentinian III. Rather than becoming the most valued general, each aroused jealousy and suspicion of declaring independent kingdoms by their rulers. It's hard to say why Narses never invoked such suspicion and Belisarius did. Some of the Gothic tribes offered Belisarius a crown late in his first Italian campaign, which he refused, but Justinian still freaked out about it.

Procopius of Caesarea is the best (and only) source on a lot of stuff around this time, but there's also good reading at:

Teall, John L. “The Barbarians in Justinian's Armies.” Speculum. (Medieval Academy of America, Apr. 1965). Vol. 40, No. 2. 294-322.

Paul the Deacon. History of the Langobards. Trans. William D. Foulke. (Philadelphia: University of Pennsylvania, 1907)

Holmes, W.G. The Age of Justinian and Theodora. (London: Gorgias Press, 1905) Vol II

Bury. J.B. History of the Later Roman Empire. From the Death of Theodosius I to the Death of Justinian. Vol.II (London: Macmillan Press, 1958)