For example, if I curve my spine, which muscle group am I using?
Bending forwards: Rectus abdominis (the "6 pack" muscle)
Bending backwards: Erector spinae group (the muscles running up your back either side of the spine)
Bending sideways: Abdominal oblique muscles (these are on the sides, in two layers, running between the hips, rib cage, and the centre of the abs)
Twisting: Also abdominal oblique muscles