The history of the entire Empire is a sprawling topic so there aren't actually a lot of general histories (at least, not many that I would be willing to recommend here).

Warren Treadgold, A History of the Byzantine State and Society (Stanford University Press, 1997) covers the whole empire, but it's extremely long.

Robert Browning, The Byzantine Empire (Catholic University of America Press, 1980, rev. ed., 1992) is also pretty big, but short compared to Treadgold.

There are also two classics in the field, although they are quite old now:

A.A. Vasiliev, History of the Byzantine Empire (University of Wisconsin Press, 1952)

George Ostrogorsky, History of the Byzantine State, trans. Joan Hussey (Blackwell, 1968)

Otherwise, are you interested in a specific era or a specific topic? If so there are probably lots of other books that you might find useful.