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Pulsed femtosecond lasers can generate acoustic pulses propagating in solids while displaying either diffraction, attenuation, nonlinearity and/or dispersion. When acoustic attenuation and diffraction are negligible, shock waves or solitons can form during propagation. Both wave types are phonon wavepackets with characteristic length scales as short as a few nanometer. Hence, they are well suited for acoustic characterization and manipulation of materials on both ultrafast and ultrashort scales. This work presents an overview of nonlinear ultrasonics since its first experimental demonstration at the beginning of this century to the more recent developments. We start by reviewing the main properties of nonlinear ultrafast acoustic propagation based on the underlying equations. Then we show various results obtained by different groups around the world with an emphasis on recent work. Current issues and directions of future research are discussed
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