  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 K\"ahler corrections. We
find that the curvature effects are negligible while the K\"ahler 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
$Q\approx m_{\rm Pl}$ 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 $\alpha \ge 11$. This model leads to $\omega_Q\approx -0.82$
for $\Omega_{\rm m}\approx 0.3$ which is in good agreement with the presently
available data.
