Is the apparent acceleration of the Universe expansion driven by a dark energy-like component or by inhomogeneities?

Since its decovery during the late 90's, the dimming of distant SN Ia apparent luminosity has been mostly ascribed to the influence of a mysterious dark energy component. Based upon the cosmological "principle" hypothesis, this interpretation has given rise to the "concordance" model, developed in the context of a Friedmann-Lemaitre cosmology. However, a caveat of this reasoning is that the cosmological "principle" derives from a philosophical Copernican assumption and has never been tested. Furthermore, a weakness of its conclusion, i. e., the existence of a negative-pressure fluid or a cosmological constant, is that it would have profound implications for the current theories of physics. This is why we have proposed a more conservative explanation, ascribing the departure of the observed universe from an Einstein-de Sitter model to the influence of inhomogeneities. This idea has been independently developed by other authors and further enlarged to the reproduction of different cosmological data. We review here the main proposals which has been made along these lines of though and present some prospects for future developments.