Conventional laboratory experimentation provides an apparent value of hydraulic permeability which, at best, is representative of the entire sample. Nuclear magnetic resonance imaging (MRI) provides unique opportunities to probe spatial distributions of permeability at a much finer scale (Seto et al., Transp Porous Media 42:351-388, 2001). We advance the methodology for determining spatial distributions of permeability and provide, for the first time, laboratory determinations of permeability distributions with complete three-dimensional (3D) spatial resolution. We investigate new experimental designs that mitigate a possible lack of identifiability and provide for more accurate estimates of permeability. We demonstrate the application of MRI experiments and analyses that provide substantial improvements in the determination of the porosity distribution, an essential step for obtaining reliable measurements of spatially resolved velocity distributions. We investigate the use of global optimization to solve the associated inverse problem for determining permeability distributions from the measured velocity distributions. Our methodology is demonstrated with experimental data on sandstone and trabecular bone samples.