The main purpose of this first book-length survey of ontic structural realism (OSR) is to convince the reader that the ontology of the physical world is one of "structures" and not of "objects". Despite the impressive range of topics that are accurately and exhaustively presented -continuity across scientific change, the underdetermination of metaphysics by physical theories, an historical survey on 20 th structuralism, the role of models and of group theory in the representation of structures, the relationship between structures and other key metaphysical notions (objects, causation, modality, dispositions, biological individuals) -my final impression is that the main objective has not been reached.The reason has to do with the fact that the simple question: "what is physical (rather than mere mathematical) structure?" has received at best a very vague answer. Consequently, aswe will see, French is forced to navigate between the Scilla of Tegmark's Pitagoreanism (2008) and the Caribdi of "blobobjectivism" (Horgan and Potrč 2008), namely the claim that the whole physical universe is a single concrete structurally complex but partless cosmos (a "blob"). The former alternative is discussed and then, understandably, rejected. While it is not clear whether French endorses the latter alternative as a plausible ontological rendering of "physical structure" (173-4, 183, 189) -he presents its pros and cons 2 -he does not seem too unsympathetic about it. In any case, I will argue that, insofar as I can understand OSR, blobobjectivism is its most coherent development but is a rather inadequate way to make sense of the ontology of contemporary physics.Given the above dilemma, the challenge of clarifying the nature of "physical structure" has not been taken up yet. In part, this follows from the fact that French often does not take stock among the various responses that he discusses to defend OSR from foreseeable obections. His review of the literature is always accompanied by new arguments, but he plays defensively:1 Thanks to Angelo Cei and Elena Castellani for their critical comments on a previous draft of 2 I think this follows despite the fact that French does not endorse Horgan and Potrč's contextualist semantics.