Very enjoyable, though I've only read the first 3. A few minor problems here and there (there's spoilers in this, of course). For example, there was a reference to the Gothic campaign, even though that was averted by the war with the Malwa. Also, even with all their technology, doesn't it seem like the Malwa, by and large, are just to dumb and cruel to have conquered so much? And notice that there's no character (with the possible exception of Domadora [sic]) thats both bad, and talented. Actually, I take that back. Theodora's a good example of that, she just happens to be on the good side.
I don't particularly care for either Theodora or Antonina in the books. Theodora started pissing me off when she basicly decided that men suck, shouldn't get to have access to gunpowder, and neither should the Persians. Antonina pissed me off from the point she ridiculed the concept of a flag, onward (especially when she leveled that monastary. sure, they might have been scum, but its a monastary, for Christ's sake). They've got the advice of a brilliant man, who's got the advice of a being that knows the entirety of human history, and they regularly assume that they know better. And the Andhra princess was a bit stuck up, but thats just part of her culture, so its not quite as annoying.
Justinian, on the other hand, redeemed himself quite nicely, IMO. I love all the various groups, like the Kushans and Rajputs. Favorite part was when Belisarius was being pursued by the Rajputs and the Pathan guide, and totally throws them off. Their reaction was priceless. I saw it coming from a mile away though.