The present paper deals with a novel approach to the derivation of constrained geometrically nonlinear shell theories which has been given in recent years by Pietraszkiewicz [1–4]. This approach has a distinct advantage over others in that it is theoretically well founded on exact polar decomposition of the shell deformation into rigid-body translation, pure stretch along the principal directions of strain and rigid-body rotation. Pietraszkiewicz [1–4] developed an exact theory of finite rotations in shells which allows for the derivation of appropriate kinematic shell relations for restricted strains and rotations of clearly defined order of magnitude. This approach has led already to a significant number of related publications [5–36] which cover various aspects of nonlinear shell theory: the derivation of first approximation theories for shells and beams undergoing small strains accompanied by moderate, large, or unrestricted rotations, associated variational principles, stability and post-buckling equations, and finite element computations. Furthermore, a similar approach to the derivation of a moderate rotation shell theory via the polar decomposition theorem has been given just recently by Naghdi and Vongsarnpigoon [37] in terms ofCosserat surface theory. Therefore, it seems to be justified to term these recent advances [1–37] based on exact polar decomposition of shell deformation with subsequent restriction of strains and rotations a new, current trend in shell theory. First, the present paper reviews briefly the progress obtained in Refs. [1–36]. Then, we present some foundations of large rotation shell theory, especially some new results which allow for the construction of variationally derivable theories. The general large rotation shell theory is simplified for problems in which the in-surface rotations remain moderate or even small. The latter variant is compared with two theories given recently by Nolte and Stumpf [9] and Pietraszkiewicz [14]. Then, for all these variants a set of basic variational principles is derived in a unified operator notation. Finally, as contribution towards the numerical justification of the present approach we present solutions for a spherical shell stability problem obtained together with Chróścielewski [63] by three-dimensional finite element analysis and compare this reference solution with those obtained by Nolte [8] on the basis of large rotation shell theories.