This chapter discusses the treatment that Professor Ruggie’s Guiding Principles offer for the responsibility to respect human rights (RtR) as applied to core companies whose affiliates’ operations infringe human rights. The issue is about a core company’s responsibility to act to address abuses that occur towards the periphery of its group or network. The fairness of globalisation is often questioned with examples from industries where business enterprises are structured along buyer-supplier, parent-subsidiary and joint venture arrangements. The concern here is that the RtR raises difficult issues when applied to a business group or network as opposed to a single business entity. The Guiding Principles are critically reviewed in section 2 for how they deal with the issue of a core company’s responsibility to act. Section 3 seeks inspiration in tort jurisprudence in an attempt to justify a responsibility to act and thus reinforce Ruggie’s foundational work on the RtR. Section 4 identifies some outstanding issues related to the RtR that could benefit from further research and attention in the post-Ruggie period.