Strange stars ought to exist in the universe according to the strange quark matter hypothesis, which states that matter made of roughly equal numbers of up, down, and strange quarks could be the true ground state of baryonic matter rather than ordinary atomic nuclei. Theoretical models of strange quark matter, such as the standard MIT bag model, the density-dependent quark mass model, or the quasi-particle model, however, appear to be unable to reproduce some of the properties (masses, radii, and tidal deformabilities) of recently observed compact stars. This is different if alternative gravity theory (e.g., non-Newtonian gravity) or dark matter (e.g., mirror dark matter) are considered, which resolve these issues. The possible existence of strange stars could thus provide a clue to new physics, as discussed in this review.