The concepts of sustainability and sustainable development are analyzed from a systems perspective. In the most general terms, sustainability of any system can be represented by a non-decreasing valuation function of the outputs of interest of the system considered. Different perspectives on the system of reference are discussed, from the extreme anthropocentric to the extreme bio- or ecocentric positions, and related to the criteria (based on the assumed substitutability between natural and manufactured capital); of very strong, strong, weak, and very weak sustainability. A set of underlying determinants of sustainability is proposed and discussed, including availability of resources, adaptability/flexibility, homeostasis, capacity of response, self-reliance, and empowerment. The concept of sustainable development is discussed and alternative theoretical perspectives that have been used in the literature are presented. The relationship between sustainability, development, nondevelopment, and maldevelopment; and material and non-material economic growth is mapped as a Venn diagram; alternative trajectories towards sustainable development for rich and poor countries are identified. Five alternative paradigms/strategies for sustainable development are summarized, showing the complexity of the process of choosing the right actions to move towards sustainable development.