Unwanted exposures to high energy or ionizing radiation can be hazardous to health. Prolonged or accumulated radiation dosage from either particle-emissions such as alpha/beta, proton, electron, neutron emissions, or high-energy electromagnetic waves such as x-rays/gamma rays, may result in carcinogenesis, cell mutations, organ failure, etc. In order to avoid occupational hazards from these kinds of exposures, traditionally heavy metals or their composites have been used to attenuate the radiation. However, protective gear made of heavy metals are not only cumbersome but also are capable of producing more penetrative secondary radiations which requires additional shielding, increasing the cost and the weight factor. Consequently, significant research efforts have been focused towards designing efficient, lightweight, cost-effective, and flexible shielding materials for protection against radiation encountered in various industries (aerospace, hospitals, and nuclear reactors). In this regard, Polymer composites have become attractive candidates for developing materials that can be designed to effectively attenuate photon or particle radiation. In this paper, we review the state-of-the-art of Polymer composites reinforced with micro-/nano-materials, for their use as radiation shields.