Recent observations seem to suggest that our Universe is accelerating implying that it is dominated by a fluid whose equation of state is negative .
Quintessence is a possible explanation .
In particular , the concept of tracking solutions permits to adress the fine-tuning and coincidence problems .
We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections .
We show that quintessence is not affected by the one-loop quantum corrections .
In the supersymmetric case where the quintessential potential is motivated by non-perturbative effects in gauge theories , we consider the curvature effects and the Kähler corrections .
We find that the curvature effects are negligible while the Kähler corrections modify the early evolution of the quintessence field .
Finally we study the supergravity corrections and show that they must be taken into account as Q \approx m _ { Pl } at small red-shifts .
We discuss simple supergravity models exhibiting the quintessential behaviour .
In particular , we propose a model where the scalar potential is given by V ( Q ) = \frac { \Lambda ^ { 4 + \alpha } } { Q ^ { \alpha } } e ^ { \frac { \kappa } { 2 } Q ^ { 2 } } .
We argue that the fine-tuning problem can be overcome if \alpha \geq 11 .
This model leads to \omega _ { Q } \approx - 0.82 for \Omega _ { m } \approx 0.3 which is in good agreement with the presently available data .