We discuss two inverse approaches to construction of fracture-flow models and their application in characterizing a fractured limestone formation, The first approach creates ''equivalent discontinuum'' models that conceptualize the fracture system as a partially filled lattice of conductors that are locally connected or disconnected to reproduce the observed hydrologic behavior. An alternative approach-i.e., ''variable aperture lattice'' models-represent the fracture system as a fully filled network composed of conductors of varying apertures or hydraulic conductivities. The fracture apertures are sampled from a specified distribution, usually log-normal, which is consistent with field data. The spatial arrangement of apertures is altered through inverse modeling to fit the available hydrologic data, such as transient pressure and/or tracer data. Unlike traditional discrete fracture-network approaches that rely on fracture geometry to reproduce flow and transport behavior, the inverse methods directly incorporate hydrologic data in deriving the fracture networks and thus naturally emphasize the underlying features that impact fluid flow and transport. However, hydrologic models derived by inversion are nonunique in general. We have addressed such nonuniqueness by examining an ensemble of models that satisfy the observation data within acceptable limits. We then determine properties that are shared by the ensemble of models and their associated uncertainties to create a conceptual model of the fracture system. We show the fracture-flow model to be consistent with geophysical imaging.