Modulational instability of nonlinear waves in dispersive environments is known across a broad range of physical media, from nonlinear optics to waves in plasmas. Since it was discovered for the surface water waves in the early 60s, it was found responsible for, or able to contribute to the topics of breaking and rogue waves, swell, ice breakup, wave-current interactions and perhaps even spray production. Since the early days, however, the argument continues on whether the modulational instability, which is essentially a one-dimensional phenomenon, is active in directional wave fields (that is whether the realistic directional spectra are narrow enough to maintain such nonlinear behaviours). Here we discuss the distinct features of the evolution of nonlinear surface gravity waves, which should be attributed as signatures to this instability in oceanic wind-generated wave fields. These include: wave-breaking threshold in terms of average steepness; upshifting of the spectral energy prior to breaking; oscillations of wave asymmetry and skewness; energy loss from the carrier waves in the course of the breaking. We will also refer to the linear/nonlinear superposition of waves which is often considered a counterpart (or competing) mechanism responsible for breaking or rogue waves in the ocean. We argue that both mechanisms are physically possible and the question of in situ abnormal waves is a problem of their relative significance in specific circumstances.