Some of the fundamental limitations of roll control and vibration isolation are analyzed and discussed. Optimum roll responses to a step input in lateral acceleration are derived from the calculus of variations. The responses show that a pendulous suspension (where the roll center is above the passengers) can be made to exert zero net lateral acceleration on passengers; whereas, a finite lateral acceleration will always be present during maneuvers of vehicles equipped with conventional suspensions (where the roll center is below the passengers). The lower limitation on roadway-induced vibration is presented as a trade-off between vibration and the clearance space between the sprung and unsprung masses or between the sprung mass and the roadway. Finally, the substantial benefits accruing from the use of preview control (where the roadway ahead of a moving vehicle is sensed) are presented.