Fully-distributed optical-fiber sensing (FDOFS) systems are developing rapidly and are offering significant advantages for measurement functions in a variety of structural applications, especially in the oil industry, the power supply industry and the aerospace industries. Polarization techniques are well established in FDOFS, and in PMD analysis for optical-fiber telecommunications. However, a major problem has been that of determining, in backscatter, the full polarization properties of a monomode optical fiber, as a function of position along the fiber, with some specified spatial resolution. This paper will present a new technique for providing this full information, and thus for measuring the distribution of any parameter, external to the fiber, which can modify its polarization behavior. As a result, for example, it becomes possible to measure simultaneously the distributions of temperature and of the full strain field, comprising, in the latter case, the longitudinal and the two transverse components of strain, plus the shear (or differential transverse) strain. Magnetic field and electric field measurements also become more readily accessible. The technique comprises a conceptual extension of POTDR, and necessitates on-line processing. Details of the physical principles, the algorithms and the polarimetry will be presented, together with results illustrating the measurement accuracies which can be achieved. The potential for further development, and application to both distributed sensing in smart structures and to PMD diagnostics in optical telecommunications, will be reviewed.