  The van der Waals quintessence equation of state is an interesting scenario
for describing the late universe, and seems to provide a solution to the puzzle
of dark energy, without the presence of exotic fluids or modifications of the
Friedmann equations. In this work, the construction of inhomogeneous compact
spheres supported by a van der Waals equation of state is explored. These
relativistic stellar configurations shall be denoted as {\it van der Waals
quintessence stars}. Despite of the fact that, in a cosmological context, the
van der Waals fluid is considered homogeneous, inhomogeneities may arise
through gravitational instabilities. Thus, these solutions may possibly
originate from density fluctuations in the cosmological background. Two
specific classes of solutions, namely, gravastars and traversable wormholes are
analyzed. Exact solutions are found, and their respective characteristics and
physical properties are further explored.
