Globally, soil salinity has been on the rise owing to various factors that are both human and environmental. The abiotic stress caused by soil salinity has become one of the most damaging abiotic stresses faced by crop plants, resulting in significant yield losses. Salt stress induces physiological and morphological modifications in plants as a result of significant changes in gene expression patterns and signal transduction cascades. In this comprehensive review, with a major focus on recent advances in the field of plant molecular biology, we discuss several approaches to enhance salinity tolerance in plants comprising various classical and advanced genetic and genetic engineering approaches, genomics and genome editing technologies, and plant growth-promoting rhizobacteria (PGPR)-based approaches. Furthermore, based on recent advances in the field of epigenetics, we propose novel approaches to create and exploit heritable genome-wide epigenetic variation in crop plants to enhance salinity tolerance. Specifically, we describe the concepts and the underlying principles of epigenetic recombinant inbred lines (epiRILs) and other epigenetic variants and methods to generate them. The proposed epigenetic approaches also have the potential to create additional genetic variation by modulating meiotic crossover frequency.