We systematically describe an approach to estimate the large-scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. We call this approach seismicity-based reservoir characterization (SBRC). A simple variant of the approach is based on the hypothesis that the triggering front of hydraulically-induced microseismicity propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium. The permeability tensor of this effective medium is the permeability tensor upscaled to the characteristic size of the seismically active heterogeneous rock volume. We show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group-velocity surface of the lowfrequency anisotropic, second-type Biots wave (i.e., slow wave). Further, we generalize SBRC for 3-D mapping of the permeability tensor of heterogeneous reservoirs and aquifers. For this we apply an approach similar to the geometric optics approximation. We derive an equation describing kinematic aspects of triggering-front propagation in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media, the inversion for the hydraulic properties of rocks follows from a direct application of this equation. In the case of an anisotropic heterogeneous medium, only the magnitude of a global effective permeability tensor can be mapped in a 3-D spatial domain. We demonstrate the method on several field examples and also test the eikonal equation-based inversion.