We analyze the characteristics of polarity in unsupported nanoribbons with zigzag edges, by a combination of analytic models, semiempirical Hartree-Fock simulations, and first-principles approach. We consider two materials with widely different ionic-covalent character, MgO and MoS2, and two polarity healing mechanisms: the so-called electronic compensation in ribbons with pristine edges, and ionic compensation in ribbons with an adequately chosen density of missing edge ions. The general expression of compensating charges, the edge metallization and spin polarization in the electronic mechanism, and the efficiency of the ionic mechanism are similar to those known in thin films and at polar surfaces. Differences, however, exist and are related to the low dimensionality, the atomic structure, and the strong undercoordination of edge atoms in nanoribbons. Polarity signatures are specified and a discussion of the possible origins of metallic edge states in these low dimensional objects is provided.