A major risk from exposure to space radiation is the induction of cancer and it is from estimates of this risk that the maximum career flight times of NASA space crew members are restricted by a permissible exposure limit. For the purpose of demonstrating compliance with the career limit, NASA has developed a cancer risk projection model for exposure-induced fatal cancer, in which the formulation and numerical values of the quality factor (QFNASA) are substantially different from those of the quality factor (Q) or radiation weighting factor (wR) routinely applied for radiation protection on earth. The quality factor is used to account for the increased effectiveness of radiations of high linear energy transfer (LET), compared to the effectiveness of low-LET γ-rays derived from epidemiological studies of the atomic-bomb survivors. The need for a special approach for space radiation is dictated by the special characteristics of the charged particles from solar radiation and especially the charged particles of high energy and charge (HZE) in galactic cosmic rays (GCR). This article considers aspects of radiation track structure in relation to the relative biological effectiveness (RBE) of HZE particles and the quality factor used for space radiation. The NASA quality factor (QFNASA) is composed of two terms, which can be interpreted as broadly representing the low- and the high-ionization-density components of the HZE particle tracks. These are discussed in turn as they relate to available experimental evidence on the biological effectiveness of such components. Also briefly described are subsequent published proposals for a reformulation of the quality factor to relate more directly to the acute γ-ray exposures from the atomic bombs and for further refinement of the parameter values (and their uncertainties) that determine the shape of the quality factor function. Other recent developments are also mentioned.