## 1 Introduction  
According to the European project called GRAPHENE Flagship ([[http://graphene-flagship.eu/](http://graphene-flagship.eu/)]([http://graphene-flagship.eu/](http://graphene-flagship.eu/))), graphene and related systems are expected to give rise to new materials and devices for information and communications technology, energy saving, and human health improvement at the horizon 2020. This technological revolution will take time: the main applications of graphene are still several years from now. From a strict fundamental point of view, graphene is a two-dimensional material whose crystalline order cannot survive in free space at the thermodynamic limit (lateral dimensions \(\rightarrow~{}\infty\)) [1]. Both electron diffraction experiments [2] and atomistic calculations [3,4] demonstrate indeed that suspended graphene ripples spontaneously, with typical lateral size between 5 and 10 nm. The situation changes when graphene is deposited on a solid surface, thanks to the interaction with the substrate. Graphite is the best illustration of this effect: its topmost (0001) atomic plane can be very flat, as demonstrated by numerous STM topographical images of highly ordered pyrolytic graphite. However, viewing graphene as a perfect flat sheet on a substrate device can be far from reality [5]. In graphene-based devices, mechanical stress is almost unavoidable. For some applications, this fact cannot be ignored: strain has indeed direct effects on the electronic properties of graphene [6,7]. These effects may become an advantage when used to tailor the transport [8] or other properties. After transfer to a substrate like SiO\({}_{2}\), graphene deformation may become important when there is a large amount of excess material. Wrinkles and folds then form locally [9], which impact the transport properties [5]. Strain also affects the Raman spectra of graphene [10], which is not without consequence given the fact that Raman spectroscopy is widely used in this context as characterization tool. In return, the change of the Raman spectrum induced by strain can be used to measure its characteristics [11,12], provided a quantitative theory of the Raman cross section be available [13,14]. These examples demonstrate how important it is to understand, measure and control the deformation of a graphene overlayer. Numerous theoretical calculations, either based on empirical potential or on sophisticated _ab-initio_ methods, have been--and still are--performed to study the mechanical properties of graphene (see Section 4 and reference herein). In parallel, continuous-medium elasticity is applied either to predict or to interpret results of measurements or of computer simulations. It is interesting to point out that many applications of elasticity to graphene and related nanostructures published in the literature are based on the Euler beam theory. The later demands macroscopic parameters such as the thickness of graphene, which is an ambiguous concept [15]. Plate theory is more appropriate to graphene and can be formulated in such a way that it relies on parameters that, non only have a sound physical ground [16], but also can be measured or calculated. Getting the best set of parameters is difficult, however, and far from being completed. On the one hand, experimental measurements of the elastic response of nanostructures by nanomechanics is still challenging (see Section 5). On the other hand, \"virtual experiments\" performed on the computer may lead to scattered data owing to the shape, size and boundary conditions applied to the sample [17]. The present paper aims at formulating the problem of elasticity of graphene within the well-established Kichhoff-Love plate theory, with a clear definition of the few elastic constants it relies on. Without targeting exhaustivity, a critical review of measured and calculated elastic constants is presented. The main result of this review is a comparative table of available data (see Table 1).