  We present a state-of-the-art calculation of the next-to-leading-order
electroweak corrections to ZZ production, including the leptonic decays of the
Z bosons into $\mu^+\mu^-\mathrm{e}^+\mathrm{e}^-$ or $\mu^+\mu^-\mu^+\mu^-$
final states. We use complete leading-order and next-to-leading-order matrix
elements for four-lepton production, including contributions of virtual photons
and all off-shell effects of Z bosons, where the finite Z-boson width is taken
into account using the complex-mass scheme. The matrix elements are implemented
into Monte Carlo programs allowing for the evaluation of arbitrary differential
distributions. We present integrated and differential cross sections for the
LHC at 13 TeV both for an inclusive setup where only lepton identification cuts
are applied, and for a setup motivated by Higgs-boson analyses in the
four-lepton decay channel. The electroweak corrections are divided into
photonic and purely weak contributions. The former show the well-known
pronounced tails near kinematical thresholds and resonances; the latter are
generically at the level of $\sim-5\%$ and reach several $-10\%$ in the
high-energy tails of distributions. Comparing the results for
$\mu^+\mu^-\mathrm{e}^+\mathrm{e}^-$ and $\mu^+\mu^-\mu^+\mu^-$ final states,
we find significant differences mainly in distributions that are sensitive to
the $\mu^+\mu^-$ pairing in the $\mu^+\mu^-\mu^+\mu^-$ final state. Differences
between $\mu^+\mu^-\mathrm{e}^+\mathrm{e}^-$ and $\mu^+\mu^-\mu^+\mu^-$
channels due to interferences of equal-flavour leptons in the final state can
reach up to $10\%$ in off-shell-sensitive regions. Contributions induced by
incoming photons, i.e. photon-photon and quark-photon channels, are included,
but turn out to be phenomenologically unimportant.
