The amount of biomedical data collected and stored has grown significantly. Analyzing these extensive amounts of data cannot be done by individuals or single organizations anymore. Thus, the scientific community is creating global collaborative efforts to analyze these data. However, biomedical data is subject to several legal and socioeconomic restrictions hindering the possibilities for research collaboration. In this paper, we argue that researchers require new tools and techniques to address the restrictions and needs of global scientific collaborations over geo-distributed biomedical data. These tools and techniques must support what we call Fully Distributed Collaborations (FDC), which are research endeavors that harness means to exploit and analyze massive biomedical information collaboratively while respecting legal and socio-economical restrictions. This paper first motivates and discusses the requirements of FDCs in the context of a research collaboration on the development of diagnostic and predictive tools for the risk of intracranial aneurysm formation and rupture (the ICAN project). The paper then presents a taxonomy classifying the current tools and techniques for biomedical analysis with respect to the proposed requirements. The taxonomy considers three key architectural features to support FDC scenarios: data and computation placement, Privacy and Security, and Performance and Scalability. The review reveals new research opportunities to design tools and techniques for multi-site analyses encouraging scientific collaborations while mitigating technical and legal constraints.