This chapter shows the intuitive side and also the unintuitive side of dominance. If one needs much iteration, things become less intuitive, in that they obtained strategies rest too heavily on an assumption of crossed rationality, which is completely strange. The chapter applies dominance to all pay auctions and to the Fort Boyard sticks game. It turns to iterated dominance and applies it to the ascending all pay auction. The chapter shows that the strange result obtained derives from the high degree of crossed rationality required by iterated elimination. It highlights that dominance is a quite powerful tool that can lead to optimal behaviour in some complicated games. The chapter shows that in the prisoner's disks game, iterated strict dominance leads to suppressing branches in the game tree so as to progressively get a structure that naturally leads to the optimal behaviour.