We are continuing to invent, develop, and translate novel Magnetic Resonance Imaging (MRI) methods from the bench to bedside. Specifically, we continue to explore new ways to assess tissue structure and architecture in vivo and non-invasively, primarily by following the water, with the aim of enabling applications in the neurosciences and biomedical research communities, and translating these novel approaches to the clinic to improve clinical outcomes. Diffusion Tensor MRI (DT-MRI or DTI) is the best-known imaging method we invented, developed, and successfully translated clinically in the past. It measures and maps a diffusion tensor of mobile tissue water. It produces scalar parameters that are intrinsic features of tissues without introducing contrast agents or dyes, but by following endogenous protons residing in tissue water. One DTI-derived quantity, the orientationally-averaged diffusion coefficient (or mean ADC), successfully visualizes a stroke in progress. The mean ADC is also widely used in cancer imaging worldwide to monitor tumor cellularity and many other diseases and disorders. Our development of novel diffusion anisotropy metrics, like the Fractional Anisotropy (FA), enabled white matter pathways to be visualized for the first time. The development direction-encoded color (DEC) maps of axon orientation allowed us to map white matter pathway orientation. DEC maps first revealed the orientations of the main association, projection, and commissural white matter pathways in the human brain. To assess anatomical connectivity between different functional regions in the brain, we invented, proposed, and developed DTI streamline tractography, made possible by a general mathematical framework to continuously and smoothly approximate measured discrete, noisy, diffusion tensor field data. Collectively, these methods and approaches have enabled detailed anatomical and structural analyses of the brain in vivo, which was only possible previously using laborious, invasive histological methods performed on excised tissue specimen. Our contributions to the invention and development of streamline tractography helped inspire the creation of NIH's Human Connectome Project (HCP). As DTI migrated to large, multi-center trials and studies, we began developing a battery of quantitative statistical tests to determine the statistical significance of ROI and population differences observed in our data. We developed empirical Monte Carlo and Bootstrap methods for determining features of the statistical distribution of the diffusion tensor from experimental DTI data and a novel tensor-variate Gaussian distribution that describes the variability of the diffusion tensor in an ideal DTI experiment. More recently, we developed approaches to measure uncertainties of many tensor-derived quantities, including the direction of axonal pathways using perturbation and statistical approaches. These developments collectively provide the foundation for applying powerful statistical hypothesis tests to address a wide array of important biological and clinical questions that previously could only be tackled in an ad hoc manner, if at all. More recently, we have developed sophisticated mathematical/physical models of water diffusion profiles to relate these to the MR signals we measure. This activity enables us to drill down into the voxel to infer new microstructural and architectural features of tissue (primarily white matter in the brain). One example is our composite hindered and restricted model of diffusion (CHARMED) MRI framework to measure a mean axon radius within a pack of axons, and an estimate of the intra and extracellular volume fractions. A refinement of CHARMED, AxCaliber MRI, enabled us to measure the axon diameter distribution (ADD) within white matter pathways. Sophisticated multiple pulsed field gradient (PFG) NMR and MRI sequences help us characterize microscopic anisotropy within tissues like gray matter, which are macroscopically isotropic (like a homogeneous gel). We have developed physical MRI phantoms to test and interrogate our various mathematical models describing water diffusion in complex tissues and infer distributions of size and shape of pores in biological tissue and other porous media from their MR data. Our group has applied novel fractal models to characterize anomalous diffusion processes that reveal underlying hierarchical structures. These also yield novel sources of MR contrast we plan to apply in neuroscience applications, such as in vivo (Brodmann or cytoarchitechtonic) parcellation of the cerebral cortex or clinical diagnostic applications, such as mild TBI detection, improved cancer diagnosis or brain tumor staging. We have been developing a way to characterize non-Gaussian features of the displacement distribution measured using MRI. To this end, our group continues to work on reconstructing the 'average propagator' (net displacement distribution) and features derived from it, using a relatively small number of DWIs to facilitate their clinical migration. The average propagator is the holy grail of displacement or diffusion imaging, which subsumes DTI as well as other higher-order tensor (HOT) methods. One approach we used previously was an iterative reconstruction scheme along with a priori information and physical constraints to infer the average propagator from DWI data. Another approach was to use a CT-like reconstruction method to estimate the displacement profile from DWI data. The most successful method to date, however, uses a Hermite functional basis to represent the average propagator, which compresses the amount of DWI data required while providing a plethora of new imaging parameters or stains with which to characterize microstructural features in tissues. A significant new initiative in our group has been the invention and development of several efficient and accurate 2D-MRI relaxometry/diffusometry/exchange methods. These include ways to measure correlations between diffusivity, T1 and T2, as well as exchange between and among them. From the standpoint of microstructure imaging, these approaches provide increasing evidence of the existence of multiple distinct water components within neural tissue which have been previously undetectable. Collectively, these novel methods and methodologies represent a pathway to realizing in vivo MRI histology--providing detailed microstructural and microarchitectural information about cells and tissues that otherwise could only be obtained using laborious and invasive histological or pathological techniques applied on biopsied or excised specimens. We are migrating the field of microstructure imaging to microstructure and microdynamic imaging, and in the process, are making the invisible visible.