High-power and high-energy femtosecond fiber laser usually consists of a master oscillator followed by a power amplifier. Nonlinear effects are the main factor restricting the amplified pulse energy. Although traditional chirped pulse amplification can generate femtosecond pulses with an average power of ~1 kW and a 1 mJ level pulse energy in a single large-mode-area Yb-doped fiber, the obtained pulse duration is limited to >200 fs. However, various applications require modest pulse energy (1~100 µJ) but a much shorter pulse duration (<60 fs). Such applications include high-order harmonic generation based on cavity enhancement technology to generate extreme ultra-violet pulses, multi-beam driven high-speed nonlinear optical imaging, and wide-spectrum mid-infrared optical frequency comb based on intra-pulse difference frequency generation, etc. This review paper focus on nonlinear pulse amplification techniques in ultrafast fiber laser systems. In contrast to chirped pulse amplification that reduces the nonlinear phase shift by broadening the pulse, the nonlinear amplification techniques maintain the amplified pulse duration in picosecond level to accumulate large nonlinear phase shift, resulting in a substantial spectral broadening. The amplified spectrum is several times wider than the input spectrum. The amplified pulse develops a nearly linear chirp that can be compressed to <60 fs in duration by a traditional grating pair. We describe the working principles and state of the art of four nonlinear fiber amplification technologies developed for Yb-doped fiber amplifiers: 1) self-similar parabolic pulse amplification, 2) pre-chirp managed amplification, 3) gain managed amplification, and 4) nonlinear divided-pulse amplification.In the self-similar amplification technique, the amplified pulse asymptotically evolves into a linearly chirped parabolic similariton due to the interplay of positive dispersion, self-phase modulation and gain. Such amplified pulse with linear chirp can be readily compressed by Treacy-type grating pair. The typical gain-fiber length for a parabolic pulse amplifier is several meters to ensure that the initial pulse of any shape can asymptotically develop a parabolic similariton. However, such long active fibers accumulate excessive nonlinear phase shift and leads to the onset of stimulated Raman scattering for μJ-level amplified pulse energy. Finite gain bandwidth for a short active-fiber or strong nonlinear effects for a long active-fiber limit further energy scaling. To overcome this bottleneck, this paper proposed a pre-chirp managed amplification to deliver μJ-level ultrafast pulses using short active-fibers without evolving into the self-similar regime. By finely pre-chirping the seeding pulse chirp prior to the nonlinear amplification, pre-chirp managed amplification can control the nonlinear phase shift to generate high-quality compressed pulse. Because the pre-chirp management adds one more degree of freedom, pre-chirp managed amplification has the potential to deliver energetic few-cycle pulses with a broader spectrum compared with parabolic pulse amplification. Recently proposed gain managed amplification technique allows generation of μJ-level femtosecond pulses based on evolving gain spectrum in long active-fibers. By adjusting the pump power and the Yb-doped fiber length, the gain managed amplifier can control the population inversion to optimize the longitudinally evolving gain shaping, which provides sufficient nonlinear spectral broadening to generate high-quality compressed femtosecond pulses.Although the above nonlinear amplification techniques contribute a much shorter pulse duration, the amplified pulse energy is much lower than that of an Yb-doped fiber chirped pulse amplification system. The highest pulse energy delivered by a nonlinear Yb-doped fiber amplifier is ~2 μJ based on pre-chirp managed amplification seeded by circularly polarized pulses. Further energy scaling is prevented by the onset of self-focusing. Given that the amplified pulse duration is picosecond level, the maximum pulse energy is limited to several micro-joules. Fortunately, nonlinear divided-pulse amplification offers an efficient solution for the poor energy scalability: each pulse to be amplified is split into a sequence of identical replicas. These replicas are temporally separated to reduce the peak power during the amplification and are finally assembled into an intense pulse after the amplification. Thanks to the picosecond pulse duration in the nonlinear amplification, birefringent plates can be employed to divide and recombine the pulses. Divided-pulse nonlinear fiber amplifiers based on birefringent plates can avoid spatially splitting the optical beam and thus create a compact system without any active stabilization. However, using birefringent plates imposes considerable Group-Delay Dispersion (GDD) differences among pulse replicas. The coherent combining efficiency drops quickly due to the accumulated GDD difference, which prevents further energy scaling by increasing the number of pulse replicas. To mitigate this general limit involved in nonlinear divided-pulse amplification, we propose to use composite birefringent plates to minimize the GDD difference. As one of the nonlinear divided-pulse amplification schemes, our proposed PCM-DPA technology based on composite plates is expected to deliver >100 μJ, <50 fs pulses with >100 W average power and >1 GW peak power. Furthermore, PCM-DPA combined with coherent beam combining may produce ~1 mJ, <50 fs pulses with 1 MHz repetition rate and >1 kW average power. Such kilowatt-level, high repetition rate and high-energy femtosecond laser sources hold great promise in various fields such as basic science, laser processing and national defense, and certainly open a series of new research fields.