It is critical to characterize the carrier and instantaneous frequency distribution variation in ultrafast processes, all of which are determined by the optical phase. Nevertheless, there is no method that can single-shot record the intro-pulse phase evolution of pico/femtosecond signals, to date. By analogizing holographic principle in space to the time domain and using the time-stretch method, we propose the dispersive temporal holography to single-shot recover the phase and amplitude of ultrafast signals. It is a comprehensive technology and can be applied to analyze ultrafast signals with highly complex dynamics. Encouraged by the accurate restoration of self-similar amplification of parabolic pulses, we track rogue wave and breathers' formation and evolution. The details of rogue waves emerging from the Fermi-Pasta-Ulam-Tsingou recurrence and chaotic modulation instability were experimentally demonstrated for the first time. The method provides a powerful tool for exploring ultrafast science, which may benefit many fields, including laser dynamics, ultrafast diagnostics, nonlinear optics, and so on.