The transport properties of concrete are critical to its field performance. Commonly encountered degradation mechanisms are dependent on ionic diffusivity, sorptivity, and permeability. In this paper, virtual testing of two of these concrete transport properties, diffusivity and permeability, will be reviewed. Virtual evaluations of ionic diffusion (and equivalently conductivity) will be presented as one example that spans the full range of applications, from computations on cement paste with micrometer resolution to a virtual rapid chloride permeability test (RCPT) that simulates the standard ASTM test method for conductivity of concrete cylinders. At the concrete scale, a hard core/soft shell (HCSS) microstructural model may be employed to estimate diffusion coefficients, while finite difference solutions of Rck's laws that incorporate sorption/reaction may be employed to evaluate remediation strategies for real world bridge decks. Virtual evaluations of permeability are dependent on a sufficient resolution of the pore sizes that are critical for flow under pressure. Two recent successful evaluations will be presented in this paper: the permeability of cement pastes (hydroceramics) cured at elevated temperatures, where transport is controlled by micrometer-sized pores, and the permeability of pervious concrete that is dominated by its coarse porosity (scale of mm). Many of the presented computational (virtual) tools are freely available over the Internet, either for direct access (remote computation) or for downloading.