  There is now strong evidence that the current energy density of the Universe
is dominated by dark energy with an equation of state w<-1/3, which is causing
accelerated expansion. The build-up of structure within such Universes is
subject to significant ongoing study, particularly through the spherical
collapse model. This paper aims to review and consolidate progress for
cosmologies in which the dark energy component remains homogeneous on the
scales of the structures being modelled. The equations presented are designed
to allow for dark energy with a general time-varying equation of state w(a). In
addition to reviewing previous work, a number of new results are introduced: A
new fitting formula for the linear growth factor in constant w cosmologies is
given. A new formalism for determining the critical density for collapse is
presented based on the initial curvature of the perturbation. The commonly used
approximation to the critical density for collapse based on the linear growth
factor is discussed for a general dark energy equation of state. Virialisation
within such cosmologies is also considered, and the standard assumption that
energy is conserved between turn-around and virialisation is questioned and
limiting possiblities are presented.
