Salt stress has a detrimental impact on food crop production, with its severity escalating due to both natural and man-made factors. As one of the most important food crops, wheat is susceptible to salt stress, resulting in abnormal plant growth and reduced yields; therefore, damage from salt stress should be of great concern. Additionally, the utilization of land in coastal areas warrants increased attention, given diminishing supplies of fresh water and arable land, and the escalating demand for wheat. A comprehensive understanding of the physiological and molecular changes in wheat under salt stress can offer insights into mitigating the adverse effects of salt stress on wheat. In this review, we summarized the genes and molecular mechanisms involved in ion transport, signal transduction, and enzyme and hormone regulation, in response to salt stress based on the physiological processes in wheat. Then, we surveyed the latest progress in improving the salt tolerance of wheat through breeding, exogenous applications, and microbial pathways. Breeding efficiency can be improved through a combination of gene editing and multiple omics techniques, which is the fundamental strategy for dealing with salt stress. Possible challenges and prospects in this process were also discussed.