This paper describes techniques for high-energy laser pulse amplification in multi-PW femtosecond laser pulses. Femtosecond laser pulses can be generated and amplified in laser media with a broad emission spectral bandwidth, like Ti:sapphire crystals. By chirped pulse amplification (CPA) techniques, hundred-Joule amplified laser pulses can be obtained. Multi-PW peak-power femtosecond pulses are generated after recompression of amplified chirped laser pulses. The characteristics and problems of large bandwidth laser pulses amplification in Ti:sapphire crystals are discussed. An alternative technique, based on optical parametric chirped pulse amplification (OPCPA) in nonlinear crystals, is presented. Phase-matching conditions for broad bandwidth parametric amplification in nonlinear crystals are inferred. Ultra-broad phase matching bandwidth of more than 100 nm, able to support the amplification of sub-10 fs laser pulses, are demonstrated in nonlinear crystals, such as Beta Barium Borate (BBO), Potassium Dideuterium Phosphate (DKDP), and Lithium Triborate (LBO). The advantages and drawbacks of CPA amplification in laser crystals and OPCPA in nonlinear crystals are discussed. A hybrid amplification method, which combines low-medium energy OPCPA in nonlinear crystals with high energy CPA in large aperture laser crystals, is described. This technique is currently used for the development of 10-PW laser systems, with sub-20 fs pulse duration and more than 1012 intensity contrast of output femtosecond pulses.