There is abundant experimental, theoretical and computational evidence that certain constrained turbulent fluid systems self-organize into large-scale structures. Examples include two-dimensional (geostrophic) fluids, guiding-centre plasmas and pure-electron plasmas, as well as two- and three-dimensional magnetofluids such as reversed-field pinches and spheromaks. The theoretical understanding of relaxation phenomena is divided into two quite different constructs: selective decay and maximal entropy. Theoretical foundations of both of these principles are largely due to Montgomery and his collaborators. In this paper, selective decay and maximal entropy theories of turbulent relaxation of fluids are reviewed and experimental evidence is presented. Experimental evidence from both 2D fluids and from 3D magnetofluids is consistent with the selective decay hypothesis. However, high-resolution computational evidence strongly suggests that formation of large-scale structures is dictated by maximal-entropy principles rather than selective decay.