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The development of a European index of territorial cohesion is both a scientific issue (exploration of possible solutions) and a political issue (potential use of the indicator to allocate aid to disadvantaged regions). This paper presents the first discussions on the issue within the framework of the ESPON 3.2 programme and emphasises the many traps raised by an attempt to construct such an index. A first review of existing work in the field of composite human development and sustainable development indices shows the extreme variety of possible solutions. A transposition of the HDI methodology to the European regional data in the second report on cohesion is proposed in order to assess its limitations and implications. The main innovation of the ESPON programme consists in taking the spatial dimension of the concept of territorial cohesion into account. This objective is illustrated by two exploratory studies: an attempt at an iterative redefinition of the “Pentagon” using territorial discriminant analysis; and a proposition of multivariate analysis of territorial discontinuities.