In 1972 and 1973 several groups observed during solar quiet times enhanced fluxes of helium, oxygen, and nitrogen at energies of ~10 MeV/nuc (N, O) and ~ <50 MeV/nuc (He), respectively. These flux increases showed peculiar elemental abundances and energy spectra, e.g. a C/O ratio =< 0.1 at ~10 MeV/nuc, significantly different from the abundances of solar energetic particles and galactic cosmic rays. Since then, this ''anomalous'' cosmic ray component (ACR) has been studied extensively and several elements have been found (He, N, O, Ne, Ar, and, to lesser extent, H and C) whose energy spectra show anomalous increases above the quiet time solar and galactic energetic particle spectrum. There have been a number of models proposed to explain the ACR component. The presently most plausible theory for the origin of ACR ions identifies neutral interstellar gas as the source material. After penetration into the inner heliosphere, the neutral particles are ionized by solar UV radiation and by charge exchange reactions with the solar wind protons. After ionization, the now singly charged ions are picked up by the interplanetary magnetic field, and are convected with the solar wind to the outer solar system. There the ions are accelerated to high energies, possibly at the solar wind termination shock, and then propagate back into the inner heliosphere. A unique prediction of this model is that ACR ions should be singly ionized. Meanwhile, several predictions of this model have been verified, e.g. low energy pickup ions have been detected and the single charge of ACR ions in the energy range of ~10 MeV/nucleon has been observed. In this paper the present status of experimental and theoretical results on the ACR component, and constraints on the acceleration process derived from the newly available ACR ionic charge measurements will be reviewed, with an emphasis on new results from Ulysses and SAMPEX.