Soil salinization is a severe abiotic stress that negatively affects plant growth and development, leading to physiological abnormalities and ultimately threatening global food security. The condition arises from excessive salt accumulation in the soil, primarily due to anthropogenic activities such as irrigation, improper land uses, and overfertilization. The presence of Na⁺, Cl−, and other related ions in the soil above normal levels can disrupt plant cellular functions and lead to alterations in essential metabolic processes such as seed germination and photosynthesis, causing severe damage to plant tissues and even plant death in the worst circumstances. To counteract the effects of salt stress, plants have developed various mechanisms, including modulating ion homeostasis, ion compartmentalization and export, and the biosynthesis of osmoprotectants. Recent advances in genomic and proteomic technologies have enabled the identification of genes and proteins involved in plant salt-tolerance mechanisms. This review provides a short overview of the impact of salinity stress on plants and the underlying mechanisms of salt-stress tolerance, particularly the functions of salt-stress-responsive genes associated with these mechanisms. This review aims at summarizing recent advances in our understanding of salt-stress tolerance mechanisms, providing the key background knowledge for improving crops’ salt tolerance, which could contribute to the yield and quality enhancement in major crops grown under saline conditions or in arid and semiarid regions of the world.