Water-in-salts are a new family of electrolytes that may allow the development of aqueous Li-ion batteries. They have a structure that is reminiscent of ionic liquids, and they are characterized by a high concentration of ionic species. In this work, we study their transport properties and how they evolve with concentration by using molecular dynamic simulations. We first focus on the choice of the force field. By comparing the simulated viscosities and self-diffusion coefficients with experimental measurements, we select a set of parameters that reproduces well the transport properties. We then use the selected force field to study in detail the variations of the self and collective diffusivities of all the species as well as the transport number of the lithium ion. We show that correlations between ions and water play an important role over the whole concentration range. In the water-in-salt regime, the anions form a percolating network that reduces the cation-anion correlations and leads to rather large values for the transport number compared to other standard electrolytes.