Research in quantitative whole breast ultrasound imaging has been developing rapidly. Recently we published results from 2D transmission inverse scattering algorithms, based on optimization, incorporating diffraction, refraction, and limited multiple scattering effects, using data collected from an early prototype, which showed the feasibility of high resolution quantitative imaging of the breast tissue speed and attenuation, and concomitant refraction corrected reflection imaging. However, artifact problems in speed and attenuation result from the 2D algorithms, and the data characteristics. The reflection algorithm uses the speed map to model refractive effects of rays, so these artifacts are unacceptable. The 3D inverse scattering algorithm presented here, using data from a new prototype, overcomes most of these artifacts. We then use a 3D refraction corrected 360 degree compounded reflection algorithm for high resolution speckle free reflection images. We discuss the transmission and reflection algorithms and the advanced scanner used to collect the data, as well as initial clinical results from the Mayo Clinic, Breast Cancer Imaging Center, Orange County, and the University California, San Diego. We show examples of fibroadenomas, calcifications, cancers (IDC), in dense, fatty and average breast tissue, and compare these with hand-held ultrasound, MRI and mammography, where available.