The development of fiber optical parametric oscillators (FOPO) based on highly nonlinear dispersionshifted fiber is reviewed in this paper. Firstly, the background and motivation are introduced, and it is pointed out that the FOPO is promising to act as optical source in non-conventional wavelength bands. Subsequently, the context focuses principally on the problem of inherent multiple-longitudinal-mode characteristic of FOPO and the corresponding solutions to it. The primary technique is by locking the phase of multiple longitudinal modes. The first reported actively mode locked FOPO is also presented in this article. However, it is not probable to realize passively mode locked FOPO because of the random phase dithering of the pump required for suppressing stimulated Brillouin scattering. Furthermore, a regeneratively mode locked FOPO is demonstrated, which can generate wide band tunable radiation in nonconventional wavelengths. Besides mode locked FOPO, the single-longitudinal-mode FOPO is also introduced. Finally, potential future directions are discussed.