A clamping apparatus includes a spindle body and a nut element to be screwed together for decreasing a spacing between first and second clamping elements to clamp an object disposed therebetween. The nut element has roller bodies with a defined roller engagement structure axially rotatably secured on a receiving body of the nut element and distributed in circumferential direction. A plurality of engagement regions distributed and/or spaced apart on the spindle body each have one spindle body engagement structure. The roller engagement structures of the roller bodies engage or can engage the spindle body engagement structures of the spindle body. The nut element can be screwed to the spindle body by the mutually engaged engagement structures of the spindle body and of the roller bodies, in particular with rolling of the roller bodies on the spindle body. An apparatus and a vise having the clamping apparatus are also provided.