In 3d animation industry, who is the person do rigging? Modeler or Animator?
Occasionally 3D artists have to take on multiple roles (most common with smaller teams) so you might see one person modeling, rigging, animating, etc., but burnin is right: typically there’s a “rigger” artist dedicated solely to creating character and prop rigs.
… and this person will be heavily involved with many different other groups: the modelers, the animators, maybe cinematographers and other production-planners. The rigger is the one who “gives the rest of 'em the knobs that they can twist and the buttons they can push.” Also concerned that the resulting contraption will perform correctly and convincingly from all camera-angles that will be used. (Implicit in this job description is also the ability to “think on one’s feet” when … not if … a change is needed and that change must not alter the many hours’ worth of work that has already been laboriously computed.)
The position is often very senior because, as you can see, it is “highly pervasive.” It touches a great many other things. It needs technical expertise, patience, grace, style … and politics. 
There are also the Level Designers who focus on the setting and props for the characters.