Abstract: In recent years, accelerated reconstruction based on model-driven deep learning has become an important technical route for fast magnetic resonance imaging. Its key idea is to learn more expressive image priors using neural networks, thereby constraining the ill-posed inverse problem under undersampled conditions. In addition to conventional priors such as sparsity and low-rankness, magnetic resonance images also contain geometric structural information, including organ morphology, tissue boundaries, structural symmetry, and motion-induced deformation. Such information exhibits relative stability and consistency across individual anatomical variations, imaging conditions, and motion states, and can be summarized as geometric invariance representation. Explicitly introducing and effectively utilizing geometric invariance representation can provide structural constraints for the reconstruction process, improve the anatomical plausibility, robustness, and cross-scenario generalization of reconstructed results, and has become an important research direction in prior modeling for deep magnetic resonance imaging. Therefore, this review focuses on the modeling and utilization of geometric invariance representation, systematically summarizes the research progress of equivariant convolutional networks, parameterized convolutions, and deformable convolutions, and discusses how these methods introduce geometric priors at the levels of network architecture, convolutional kernel representation, and sampling mechanism, with the aim of providing reference for structural prior design in deep magnetic resonance imaging.