A device for moving the back and core muscles while sitting includes a rocking assembly that sits atop a base assembly, and optionally a height adjustment mechanism between the rocking assembly and the base assembly. The rocking assembly further includes a rocking mechanism that sits between a base plate or platform and a seat. The rocking mechanism can be, for example, a hollow or solid hemispheric- or dome-shaped rocking mechanism, an eccentric bicylinder rocking mechanism, and/or a rocking mechanism based on an arrangement of halfpipe members. The rocking mechanisms of the exercise chair allow to the seat to rock, wobble, and/or swivel with a side-to-side rocking motion, a front-to-back rocking motion, or both a side-to-side rocking motion and a front-to-back rocking motion.