To enhance sensing or communication capabilities, the utilization of extremely large multiple-input multiple-output transceiver arrays (EL-MIMO-TAs) with high array degrees-of-freedom (DoFs) holds significant promise for future applications, such as integrated sensing and communications systems. However, the implementation of EL-MIMO-TAs may face the problem of mutual coupling. It also necessitates a substantial number of radio frequency chains, leading to undesirable hardware costs. Consequently, there has been a growing interest in sparse array designs aimed at reducing mutual coupling and hardware expenses while maintaining a constant array DoFs. Nevertheless, conventional sparse arrays primarily benefit from spatial DoFs alone. A shift toward the development of sparse polarimetric arrays has emerged, offering low mutual coupling, and enhanced spatial DoFs along with the ability to exploit the polarimetric characteristics of electromagnetic waves. This chapter explores different strategies for designing sparse polarimetric arrays, focusing on the sparsity of array element positions—specifically, non-uniform, uniform, and hybrid non-uniform and uniform sparsity. Additionally, it introduces a novel method for estimating multi-dimensional parameters based on the reconstructed covariance matrix through data fitting, emphasizing low computational complexity. A new beamformer in the spatial-polarimetric joint domain is also presented, showcasing its ability to suppress main-lobe interferences and improved beamforming performance from a sparse reconstruction perspective.