The anomalous component, observed first in the early 1970's, poses a significant challenge to our understanding of cosmic-ray origin and transport. It appears at present that most of its observed properties, including composition, time-dependence, energy spectrum and spatial gradients, can be understood as a natural consequence of the acceleration of freshly-ionized interstellar neutral atoms at the termination shock of the solar wind. It therefore provides a valuable probe of the outer heliosphere. The models show significantly-improved agreement with the data if the polar heliospheric magnetic field is modified to be larger and more transverse, as suggest recently. The models also suggest that the energy density of the anomalous component may modify the solar wind flow and shock if the shock is at a heliospheric distance which is significantly greater than 80-100 A.U.