We review several algorithms for obtaining quantitative reconstructions of weakly scattering objects from measured intensity data. These algorithms represent an extension of the usual techniques of diffraction tomography to cases where phase information cannot be measured or is otherwise unavailable, such as in the optical regime. The algorithms we present take advantage of the holographic recording geometry of diffraction tomography -- where the interference of the scattered wave with the incident wave is measured -- and generate a quantitative reconstruction of the scattering object by numerically recovering the phase of the scattered field prior to the tomographic reconstruction step. Phase recovery is performed non- iteratively using two intensity measurements. We compare this algorithm to a direct reconstruction algorithm within the Rytov approximation for the tomographic reconstruction of the index of refraction distribution of an optical fiber from simulated intensity data. These algorithms extend the practical range of diffraction tomography and inverse scattering by allowing reconstruction from phase-less scattering data using support constraints or additional measurements.