Abstract: The descriptions and applications of the rotations and spins of deforming bodies, the measures and applications of strains and strainings, and the objective' derivatives of stresses are thiee interrelated important aspects in nonlinear field thetories of mechanics.Daring the last ten years, they have been extensively studied and great progress has been made. In this paper a comprehen- sive review on those three aspects is given, which includes also contributions of the authors.