- A review of recent studies on a new mechanism of generation of large-scale magnetic field in a sheared turbulent plasma is presented. This mechanism is associated with the shear-current effect which is related to the WJ-term in the mean electromotive force. This effect causes the generation of the large-scale magnetic field even in a nonrotating and nonhelical homogeneous sheared turbulent convection whereby the a effect vanishes (where W is the mean vorticity due to the large-scale shear motions and J is the mean electric current). It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current effect. However, there is no dynamo action due to the shear-current effect for small hydrodynamic and magnetic Reynolds numbers even in a turbulent convection, if the spatial scaling for the turbulent correlation time is tðk Þ/ k � 2 , where k is the small-scale wave number. We discuss here also the nonlinear mean-field dynamo due to the shear-current effect and take into account the transport of magnetic helicity as a dynamical nonlinearity. The magnetic helicity flux strongly affects the magnetic field dynamics in the nonlinear stage of the dynamo action. When the magnetic helicity flux is not small, the saturated level of the mean magnetic field is of the order of the equipartition field determined by the turbulent kinetic energy. The obtained results are important for elucidation of origin of the large-scale magnetic fields in astrophysical and cosmic sheared turbulent plasma. r 2007 Elsevier Ltd. All rights reserved.