We present a review of nonlinear Alfvenic solitary and shock waves in a magnetized electron-ion plasma. The dynamics of these nonlinear dispersive Alfven waves is governed by the two-fluid equations, coupled with Faraday's and Ampere's laws. First, we demonstrate the existence of large amplitude compressional Alfvenic solitary and shock waves propagating across the external magnetic field in a warm electron-ion magnetoplasma. It is found that these nonlinear structures can exist in well defined speed ranges above the Alfven speed, and their widths are several times larger than the electron skin depths. Second, we study the formation of nonlinear slow magnetosonic solitary (SMS) waves propagating almost perpendicular to the external magnetic field direction. The propagation speed of the SMS waves is below the Alfven speed and their width is a few ion skin depths in a collisionless magnetoplasma. The nonlinear dispersive Alfven waves, as discussed here, can be associated with localized electromagnetic field excitations in magnetized laboratory and space plasmas that are composed of magnetized electrons and ions.
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