Because the reactor pressure vessel (RPV) represents the first structural line of defense against the release of radiation to the public, the design and fabrication of the RPV for any nuclear reactor facility is performed at very high standards in accordance with consensus codes that are based on mechanical and physical properties of the steels used to construct the vessel. Nuclear RPVs may weigh up to 800 tons with wall thicknesses up to approximately 330 mm and are clad on the inside with stainless-steel weld metal and given a final post-weld heat treatment. The RPV is a unique structural component in that it operates under high pressures and temperatures and is exposed to relatively high neutron radiation. Although typical RPV steels and welds have excellent fracture toughness at room temperature and above when put into service, the degrading effects of high-energy neutron irradiation can cause levels of irradiation-induced embrittlement in radiation-sensitive materials of concern for the structural integrity of the RPV. In recent decades, remarkable progress has been made in developing a mechanistic understanding of irradiation embrittlement. This progress includes developing physically based and statistically calibrated models of Charpy V-notch-indexed transition temperature shifts based on results from RPV surveillance programs complemented by significant results from comprehensive research experiments performed in test reactors. In addition, advances in elastic-plastic fracture mechanics allow for a relatively small number of relatively small specimens to characterize the fracture toughness of RPV steels with statistical confidence. This paper presents a review of the primary mechanical properties, test procedures, examples of applicable codes and standards, and specimen types used to characterize RPV steels and welds, the effects of neutron irradiation on those most relevant mechanical properties, and a brief review of the effects of thermal aging on RPV materials. The paper closes with a summary.