The ocean exerts a pervasive influence on Earth's environment. It is therefore important that we learn how this system operates (NRC, 1998b; 1999). For example, the ocean is an important regulator of climate change (e.g., IPCC, 1995). Understanding the link between natural and anthropogenic climate change and ocean circulation is essential for predicting the magnitude and impact of future changes in Earth's climate. Understanding the ocean, and the complex physical, biological, chemical, and geological systems operating within it, should be an important goal for the opening decades of the 21st century. Another fundamental reason for increasing our understanding of ocean systems is that the global economy is highly dependent on the ocean (e.g., for tourism, fisheries, hydrocarbons, and mineral resources) (Summerhayes, 1996). The establishment of a global network of seafloor observatories will help to provide the means to accomplish this goal. These observatories will have power and communication capabilities and will provide support for spatially distributed sensing systems and mobile platforms. Sensors and instruments will potentially collect data from above the air-sea interface to below the seafloor. Seafloor observatories will also be a powerful complement to satellite measurement systems by providing the ability to collect vertically distributed measurements within the water column for use with the spatial measurements acquired by satellites while also providing the capability to calibrate remotely sensed satellite measurements (NRC, 2000). Ocean observatory science has already had major successes. For example the TAO array has enabled the detection, understanding and prediction of El Nino events (e.g., Fujimoto et al., 2003). This paper is a world-wide review of the new emerging "Seafloor Observatory Science", and describes both the scientific motivations for seafloor observatories and the technical solutions applied to their architecture. A description of world-wide past and ongoing experiments, as well as concepts presently under study, is also given, with particular attention to European projects and to the Italian contribution. Finally, there is a discussion on "Seafloor Observatory Science" perspectives.