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Nowadays synthetic aperture radar (SAR) and multiple-input-multiple-output (MIMO) antenna systems with the capability to radiate waves in more than one pattern and polarization are playing a key role in modern telecommunication and radar systems. This is possible with the use of antenna arrays as they offer advantages of high gain and beamforming capability, which can be utilized for controlling radiation pattern for electromagnetic (EM) interference immunity in wireless systems. However, with the growing demand for compact array antennas, the physical footprint of the arrays needs to be smaller and the consequent of this is severe degradation in the performance of the array resulting from strong mutual-coupling and crosstalk effects between adjacent radiating elements. This review presents a detailed systematic and theoretical study of various mutual-coupling suppression (decoupling) techniques with a strong focus on metamaterial (MTM) and metasurface (MTS) approaches. While the performance of systems employing antenna arrays can be enhanced by calibrating out the interferences digitally, however it is more efficient to apply decoupling techniques at the antenna itself. Previously various simple and cost-effective approaches have been demonstrated to effectively suppress unwanted mutual-coupling in arrays. Such techniques include the use of defected ground structure (DGS), parasitic or slot element, dielectric resonator antenna (DRA), complementary split-ring resonators (CSRR), decoupling networks, P.I.N or varactor diodes, electromagnetic bandgap (EBG) structures, etc. In this review, it is shown that the mutual-coupling reduction methods inspired By MTM and MTS concepts can provide a higher level of isolation between neighbouring radiating elements using easily realizable and cost-effective decoupling configurations that have negligible consequence on the array's characteristics such as bandwidth, gain and radiation efficiency, and physical footprint.