Climate change gives rise to numerous environmental stresses, including soil salinity. Salinity/salt stress is the second biggest abiotic factor affecting agricultural productivity worldwide by damaging numerous physiological, biochemical, and molecular processes. In particular, salinity affects plant growth, development, and productivity. Salinity responses include modulation of ion homeostasis, antioxidant defense system induction, and biosynthesis of numerous phytohormones and osmoprotectants to protect plants from osmotic stress by decreasing ion toxicity and augmented reactive oxygen species scavenging. As most crop plants are sensitive to salinity, improving salt tolerance is crucial in sustaining global agricultural productivity. In response to salinity, plants trigger stress-related genes, proteins, and the accumulation of metabolites to cope with the adverse consequence of salinity. Therefore, this review presents an overview of salinity stress in crop plants. We highlight advances in modern biotechnological tools, such as omics (genomics, transcriptomics, proteomics, and metabolomics) approaches and different genome editing tools (ZFN, TALEN, and CRISPR/Cas system) for improving salinity tolerance in plants and accomplish the goal of "zero hunger," a worldwide sustainable development goal proposed by the FAO.