"A Brief History of Rome" shares some traits with Risk, but it is NOT a world conquest game. Not sure exactly how to describe it, but it is a "rise and fall" style of game, where the object is to try and build and defend your empire against the barbarian hordes.
People constantly confuse the game type and end up disappointed as a result, but you cannot - and are not intended to - be able to permanently conquer the map. The aim is to see how powerful/great an empire you can build before it all inevitably comes crashing down - that is the design.
Tip (to anyone who decides to try it): As with all my games, reading the manual/FAQ is very highly recommended.