The roaming mechanism in the reaction H + MgH -> Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio three-dimensional ground electronic state potential energy surface. The reaction dynamics anchored on three-dimensional normally hyperbolic invariant manifold associated with are explored by running trajectories initialized on a four-dimensional dividing surface a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase space where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. The complex forming trajectories in the HMgH well can either return to the radical channel or "roam" to the MgHH minimum from where the molecule may react.