We explore the issue of spacetime emergence in quantum gravity by articulating several levels at which this can be intended. These levels correspond to the reconstruction moves that are needed to recover the classical and continuum notion of space and time, which are progressively lost in a progressively deeper sense in the more fundamental quantum gravity description. They can also be understood as successive steps in a process of widening of the perspective, revealing new details and new questions at each step. Each level carries indeed new technical issues and opportunities, and raises new conceptual issues. This deepens the scope of the debate on the nature of spacetime, both philosophically and physically. 4 of dubious physical significance, since the dependence of ph ysical quantities on individual points in the differentiable manifold is removed by the request for diffeo morphism invariance [28], the gauge symmetry of GR. Diffeomorphism invariance is indeed a key mathematical ingre dient at the root of many of the conceptual difficulties about the nature of space and time in c lassical GR, and which have to do with the variety of possible identifications hinted at above [29, 30]. A more physical way of characterizing these difficulties is to say that they arise from the fact that every ingredient of the theory entering the definition o f ‘spacetime’, matter and metric fields, is dynamical and that the dynamics itself, and its generic solutions, do n ot select any preferred time or space direction. On the contrary, the theory admits an infi nity of equally valid local notions of time and space (that could associated to specific coordinate frames, but without attributing to the latter any special physical significance). In this sense, one can already speak of a disappearance of spa ce and time in classical relativistic gravitational theory [31]. It is bypassed, in some sense, by the use of special solutions of the dynamics, which possess global spacetime symmetries and th us select special spacetime directions. In fact, much of gravitational physics rests on the use of suc h solutions. At the conceptual level, this is already a big challenge to ou r customary conceptions of space and time, and raise many subtle issues, which form the subjec t of a vast literature in the philosophy of spacetime [32–34]. Notice that we are not distinguishing, here, between Lagran gian or Hamiltonian formulations of the theory, even though they are not strictly speaking equ ivalent (diffeomorphism symmetry is implemented in subtly different ways in the two settings, and a canonical Hamiltonian formulation requires global hyperbolicity, thus it is a priori less gene ral than the covariant, Lagrangian one). We are also not distinguishing between space and time, even t hough the absence of a preferred notion of time is especially troublesome for our usual under standing of physical dynamics and of physics more generally. These special difficulties are the ‘p roblem of time’in classical GR. These distinctions are not crucial to the main points we want to mak e in this contribution. At the quantum level, assuming a standard formulation of qua ntum mechanics, the situation is much the same, just a little worse. The kinematics has states forming a Hilbert space which encode the geometry (intrinsic and extrinsic) of spatial submanif olds (possibly forming the boundaries of the differentiable manifold) and the values and momenta of m atter fields on them, and the possible histories of the same states, thus the spacetime me tric and the matter fields for the whole manifold. The dynamics is encoded in some operator equation , taking necessarily the form of 15 A scenario of the type sketched above, we believe, will requi re serious reflections not only on the nature of space and time, but also on the renormalization group when applied to quantum gravity and on a covariant, spacetime-free understanding o f statistical mechanics. Even more clearly, it may have profound implications on the philosoph y of cosmology, that will be subject to a broadening of scope and perspective in parallel with the on e we are suggesting for the philosophy of quantum gravity. In the end, these many new conceptual issues that arise in thi s scenario are the reason to associate to it a new level of spacetime disappearance and em ergence. V. AN ANALOGY: BOSE-EINSTEIN CONDENSA TES Before concluding, we would like to offer a physical analogy of the situation outlined for quantum gravity, and of the various levels of ‘emergence’we illustr ated in this contribution. We hope this will clarify further the conceptual framework we have in min d. For more details on this example, see [88] Consider the hydrodynamic description of a fluid, with the ma in dynamical variables being the fluid density and velocity, and interesting observables being the total momentum and energy, vorticity, circulation of vortex excitations, viscosity, etc, which are functions of them. On top of the global configurations of the fluid, one has propagating excit ations over them corresponding to sound waves with their own characteristic dispersion relation. N otice that one can also consider extended versions of standard fluid hydrodynamics, including new ter ms functions of the same density and velocity fields (e.g. gradient terms); this is the case, for e xample, of superfluid hydrodynamics. In our analogy, standard hydrodynamics would be the counter part of GR, with spatiotemporal, geometric observables (volumes, areas, distances, time in tervals, curvature, etc) corresponding to various hydrodynamic observables, functions of the basic fi elds (in GR, the metric or metric and connection etc, plus matter fields, depending on the specific formulation of classical gravity one uses). From this classical theory, one can move to the quantum regim e. One could start by simply quantizing the classical theory. The resulting quantum the ory is perturbatively non-renormalizable as a quantization of sound waves