A large part of global agricultural fields, including the wheat (Triticum aestivum L.) ones, are subjected to various stresses including salinity. Given the increasing world population, finding methods and strategies that can alleviate salinity stress on crop yield production is of outmost importance. The presented review has consulted more than 400 articles related to the clean and sustainable production of wheat in saline fields affected by biological, environmental, economical, and social parameters including the important issue of climate change (global warming). The negative effects of salt stress on plant growth and the techniques, which have been so far detected to alleviate salinity stress on wheat growth have been analyzed and presented. The naturally tolerant species of wheat can use a range of mechanisms to alleviate salinity stress including sodium exclusion, potassium retention, and osmoregulation. However, the following can be considered as the most important techniques to enhance wheat tolerance under stress: (1) the biotechnological (crop breeding), biological (soil microbes), and biochemical (seed priming) methods, (2) the use of naturally tolerant genotypes, and (3) their combined use. The proper handling of irrigation water is also an important subject, which must be considered when planting wheat in saline fields. In conclusion, the sustainable and cleaner production of wheat under salt stress is determined by a combination of different parameters including the biotechnological techniques, which if handled properly, can enhance wheat production in saline fields.