  We present state-of-the-art predictions for off-shell $t\bar{t}b\bar{b}$
production with di-lepton decays at the LHC with $\sqrt{s}=13$ TeV. Results are
accurate at NLO in QCD and include all resonant and non-resonant diagrams,
interferences and finite-width effects for top quarks and $W$ bosons. We
discuss the impact of QCD corrections and assess theoretical uncertainties from
scale and PDF dependence at the integrated and differential level. Additionally
we investigate the size of contributions induced by initial-state $b$ quarks to
the NLO cross section.
