Losses are taken by morale loss which also translates into sp losses. Once a force's morale is reduced to 0, it breaks. Supply is critical. Supply lines have to be created to friendly supply sources, which are traced through friendly sp's, which are dropped off from the main force and act like depots. Forces take attrition at the beginning of the turn, and the more in the hex, the greater the loss.
Forces can also force march, with the possibility of additional losses.
The game covers the main scenarios from 1805 - 1815, with a grand campaign game. It doesn't have the economic and political complexity of Empire in Arms, but, at least in the campaign game far more playable. IMO it's an excellent game, and one that I return to periodically. But I believe that it does have a number of flaws. The seige rules are quite poor - it's too easy to assault a fortress.