Cartoon showing the dynamical arguments used in this paper to constrain unseen planets from debris discs. At least one planet is assumed to have sculpted the inner edge of each disc (brown); this could be a single large planet (red circle) or multiple smaller planets (black circles). If the disc is eccentric, then we ascribe this to perturbations by a planet on an eccentric orbit (red line). The fact that we see dust implies that debris undergoes destructive collisions, which requires the disc to have been stirred; stirring may be performed by unseen planets (although other mechanisms are also possible). Planets can induce other debris morphologies in addition to those shown here, such as warps, resonant structures, and gaps; however, for this paper we only consider the above dynamical arguments.