Muon decay rings are under study as part of an International Scoping Study (ISS) for a future Neutrino Factory. Both isosceles triangle and racetrack, shaped rings are being considered for a 20 GeV muon energy, but with upgrade potentials of 40 or 50 GeV. Both rings are designed with long straights to optimize directional muon decay. The neutrinos from muon decay pass to one or two distant detectors; the racetrack ring has one very long production straight aligned with one detector while the triangular ring has two straights which can be aligned with two detectors. Decay ring specifications and lattice studies are the primary topic of this paper. Injection, collimation, and the RF system are covered in a second contribution to these proceedings