We don't know very much at all: all the literary sources for this period are from centuries later, and the archaeology of early Rome is made difficult by the fact that most of it is buried underneath later Rome. There are basically two schools of thought about early Rome: one is that the sources are too late to be of any use, and virtually everything we hear in the legends is a later invention. The other position is that there is a core of truth to the later sources, although even Tim Cornell (✝), one of the main exponents of this line, is pretty sceptical when it comes to the monarchical period. About all we can say for certain is that before the Republic, Rome probably was ruled by kings, and some of the names passed down may be historical. There is some supporting evidence for kingship at Rome: the lapis niger is a very ancient inscribed stone which has the word recei on it, an archaic form of rex, regis, king. But barring the discovery of some pre-Republican king lists or something, we'll just never know with any certainty about the historicity of the seven kings, although that won't stop people from offering their own unconfirmable interpretations based on the source material that we do have.

✝ see his excellent The Beginnings of Rome (Routledge, 1995).