Salt stress impairs growth and yield in tomato, which is mostly cultivated in arid and semi-arid areas of the world. A number of wild tomato relatives (Solanum pimpinellifolium, S. pennellii, S. cheesmaniae and S. peruvianum) are endemic to arid coastal areas and able to withstand higher concentration of soil salt concentrations, making them a good genetic resource for breeding efforts aimed at improving salt tolerance and overall crop improvement. However, the complexity of salt stress response makes it difficult to introgress tolerance traits from wild relatives that could effectively increase tomato productivity under high soil salt concentrations. Under commercial production, biomass accumulation is key for high fruit yields, and salt tolerance management strategies should aim to maintain a favourable plant water and nutrient status. In this review, we first compare the effects of salt stress on the physiology of the domesticated tomato and its wild relatives. We then discuss physiological and energetic trade-offs for the different salt tolerance mechanisms found within the Lycopersicon clade, with a focus on the importance of root traits to sustain crop productivity.