Robustness is a pervasive property of living systems, instantiated at all levels of the biological hierarchies. As several other usual concepts in evolutionary biology, such as plasticity or dominance, it has been questioned from the viewpoint of its consequences upon evolution as well as from the side of its causes, on an ultimate or proximate viewpoint. It is therefore equally the explanandum for some enquiries in evolution in ecology, and the explanans for some interesting evolutionary phenomena such as evolvability. This epistemological fact instantiates general property of biological evolution that I call “explanatory reversibility”. In this chapter, I attempt to systematize the explanatory projects regarding robustness by distinguishing a set of epistemological questions. Are they the various expressions of one general project with specific key concepts and methods, or very disparate epistemic projects, unified by the mere homonymy of the term “robustness”? More precisely, are there specific kinds of explanations suited to explain robustness? Finally, how does robustness as an explanandum connect with other explananda in which evolutionists have been massively interested recently such as complexity, modularity or evolvability? After having initially explored various meanings of the concept of robustness and surveyed its instances in biology, I will propose a distinction between mechanical and structural explanations of robustness in evolutionary and functional biology. Then, among the latter, I will highlight the class of “topological explanations,” and the subclass of explanations based on networks, as a major explanatory tool to address robustness. Focusing on evolutionary issues, I will eventually address the “explanatory reversibility” of robustness and consider its relation to key evolutionary concepts that are also explanatorily revertible such as modularity, evolvability and complexity.