Thurstonian forced-choice modeling is considered to be a powerful new tool to estimate item and person parameters while simultaneously testing the model fit. This assessment approach is associated with the aim of reducing faking and other response tendencies that plague traditional self-report trait assessments. As a result of major recent methodological developments, the estimation of normative trait scores has become possible in addition to the computation of only ipsative scores. This opened up the important possibility of comparisons between individuals with forced-choice assessment procedures. With item response theory (IRT) methods, a multidimensional forced-choice (MFC) format has also been proposed to estimate individual scores. Customarily, items to assess different traits are presented in blocks, often triplets, in applications of the MFC, which is an efficient form of item presentation but also a simplification of the original models. The present study provides a comprehensive review of the present status of Thurstonian forced-choice models and their variants. Critical features of the current models, especially the block models, are identified and discussed. It is concluded that MFC modeling with item blocks is highly problematic and yields biased results. In particular, the often-recommended presentation of blocks with items that are keyed in different directions of a trait proves to be counterproductive considering the goal to reduce response tendencies. The consequences and implications of the highlighted issues are further discussed.