After a brief, critical review of the leading explanations proposed for the small but important subset of radio galaxies showing an X-shaped morphology (XRGs) we propose a generalized model, based on the jet-shell interaction and spin-flip hypotheses. The most popular scenarios for this intriguing phenomenon invoke either hydrodynamical backflows and over-pressured cocoons or rapid jet reorientations, presumably from the spin-flips of central engines following the mergers of pairs of galaxies, each of which contains a supermassive black hole (SMBH). We confront these models with a number of key observations and thus argue that none of the models is capable of explaining the entire range of salient observational properties of XRGs, although some of the arguments raised in the literature against the spin-flip scenario are probably not tenable. We then propose here a new scenario which also involves galactic mergers but would allow the spin of the central engine to maintain its direction. Motivated by the detailed multi-band observations of the nearest radio galaxy, Centaurus A, this new model emphasizes the role of interactions between the jets and the shells of stars and gas that form and rotate around the merged galaxy and can cause temporary deflections of the jets, occasionally giving rise to an X-shaped radio structure. Although each of the models is likely to be relevant to a subset of XRGs, the bulk of the evidence indicates that most of them are best explained by the jet-shell interaction or spin-flip hypotheses.

19 pages, major revision including two Appendices and a Table, accepted in Research in Astronomy and Astrophysics