We survey in this paper the main differences among three variants of an intramolecular model for gene assembly: the general, the simple, and the elementary models. We present all of them in terms of sorting signed permutations and compare their behavior with respect to: (i) completeness, (ii) confluence (with the notion defined in three different setups), (iii) decidability, (iv) characterization of the sortable permutations in each model, (v) sequential complexity, and (vi) experimental validation.