Linkage disequilibrium mapping of quantitative traits is a powerful method for dissecting the genetic etiology of complex phenotypes. Quantitative traits, however, often exhibit characteristics that make their use problematic. For example, the distribution of the trait may be censored, highly skewed, or contaminated with outlying values. We propose here a rank-based framework for deriving tests of gene and trait association that explicitly take censoring into account and are insensitive to skewness and outlying values. Standard methods for mapping quantitative traits do not take these characteristics into account, which leads to the discarding of valuable information or their improper application. We show how this framework can be applied in nuclear families and discuss its implementation in general pedigrees. The power and efficacy of the approach is illustrated through a series of simulation experiments in which the approach is compared to existing methods.