The discovery that the Universe is accelerating will possibly be seen in a few years 
as one of the turning points in the history of cosmology. After nearly ten years, the 
origin of the accelerated expansion is still unknown.  One possibility is that the 
Universe is permeated by a "dark energy" which gives rise to a gravitational 
repulsion.  Alternatively, perhaps the very equations of General Relativity need to be 
modified or generalized to higher-dimensional worlds and the acceleration is only 
apparent.     
 
In my talk I will first review these general ideas.  I will then introduce a new promising 
approach to understanding the nature of cosmic acceleation from large surveys of 
galaxy redshifts, presenting a first application to data from the VVDS survey.  
Specifically, I will show how measurements of linear redshift-space distortions due to 
galaxy coherent motions can be used to trace the evolution of the growth rate of 
cosmic structures f(z) at different epochs.  Combined to the classical estimates of the 
cosmic expansion rate H(z), as those from Type Ia Supernovae or  Baryonic 
Acoustic Oscillations, these observations can pinpoint the physical origin of the 
accelerated expansion, distinguishing true dark-energy models from modifications 
of the gravitation theory.