There is provided a portable, folding chair with an enhanced seat and backrest. The seat includes a suspension system that is capable of providing an enhanced range of motion in seating directions. The backrest provides enhanced support through an enlarged support surface and improved disposition of the support surface relative to the chair frame. The seat and backrest can be used together on the same chair or independently. There is also provided an alternate seat employing a suspension system that is capable of providing an enhanced range of motion in seating directions and that has a low profile to be used in situations where storage space is a significant consideration.