  Distributions of transverse momentum $p_T^{ll}$ and the angular variable
$\phi^*_\eta$ of Drell--Yan lepton pairs are measured in 20.3 fb$^{-1}$ of
proton--proton collisions at $\sqrt{s}=8$ TeV with the ATLAS detector at the
LHC. Measurements in electron-pair and muon-pair final states are corrected for
detector effects and combined. Compared to previous measurements in
proton--proton collisions at $\sqrt{s}=7$ TeV, these new measurements benefit
from a larger data sample and improved control of systematic uncertainties.
Measurements are performed in bins of lepton-pair mass above, around and below
the Z-boson mass peak. The data are compared to predictions from perturbative
and resummed QCD calculations. For values of $\phi^*_\eta < 1$ the predictions
from the Monte Carlo generator ResBos are generally consistent with the data
within the theoretical uncertainties. However, at larger values of
$\phi^*_\eta$ this is not generally the case. Monte Carlo generators based on
the parton-shower approach are unable to describe the data over the full range
of $p_T^{ll}$ and the fixed-order prediction of DYNNLO falls below the data at
high values of $p_T^{ll}$. ResBos and the parton-shower Monte Carlo generators
provide a much better description of the evolution of the $\phi^*_\eta$ and
$p_T^{ll}$ distributions as a function of lepton-pair mass and rapidity.
