We explore the nature of Business Groups, that is network-like forms of hierarchical organization between legally autonomous firms spanning both within and across national borders. Exploiting a unique dataset of 270,474 headquarters controlling more than 1,500,000 (domestic and foreign) affiliates in all countries worldwide, we find that business groups account for a significant part of value-added generation in both developed and developing countries, with a prevalence in the latter. In order to characterize their boundaries, we distinguish between an affiliate vs. a group-level index of vertical integration, as well as an entropy-like metric able to summarize the hierarchical complexity of a group and its trade-off between exploitation of knowledge as an input across the hierarchy and the associated communication costs. We relate these metrics to host country institutional characteristics, as well as to the performance of affiliates across business groups. Conditional on institutional quality, a negative correlation exists between vertical integration and organizational complexity in defining the boundaries of business groups. We also find a robust (albeit non-linear) positive relationship between a group's organizational complexity and productivity which dominates the already known correlation between vertical integration and productivity. Results are in line with the theoretical framework of knowledge-based hierarchies developed by the literature, in which intangible assets are a complementary input in the production processes.