Since 1998 we know that the Universe have been accelerating in its expansion during the last few billions years. However, a convincing theoretical explanation of this behavior is still lacking. In fact, an accelerated expansion means either that gravity becomes repulsive at the largest scales or that there exists a yet unknown cosmic fluid, named Dark Energy, that drives it. In this seminar I will focus on the second possibility and, after a general review on the problem of cosmic acceleration, I will present a model of Dark Energy based on the  Higgs field minimally coupled to gravity.