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I review the covariant construction of the general maximally supersymmetric (N=8) supergravities in four space-time dimensions. The possible deformation parameters can be identified with the components of the various possible (geometric and non-geometric) higher-dimensional fluxes. In particular, I will discuss a new class of N=8 theories in which the global scale invariance is gauged. A particular feature of these theories is an additional positive contribution to the effective cosmological constant.