High-contrast, high-resolution imaging of biomedical specimens is indispensable for studying organ function and pathologies. Conventional histology, the gold standard for soft-tissue visualization, is limited by its anisotropic spatial resolution, elaborate sample preparation, and lack of quantitative image information. X-ray absorption or phase tomography have been identified as promising alternatives enabling non-destructive, distortion-free three-dimensional (3D) imaging. However, reaching sufficient contrast and resolution with a simple experimental procedure remains a major challenge. Here, we present a solution based on x-ray phase tomography through speckle-based imaging (SBI). We demonstrate on a mouse kidney that SBI delivers comprehensive 3D maps of hydrated, unstained soft tissue, revealing its microstructure and delivering quantitative tissue-density values at a density resolution of better than 2 mg/cm³ and spatial resolution of better than 8 µm. We expect that SBI virtual histology will find widespread application in biomedicine and will open up new possibilities for research and histopathology.