  The calculation of $t\bar{t}Z$ production including leptonic decays of both
$Z$ boson and top quarks via a partially or fully off-shell calculation
represents a definite step forward towards a more accurate description of
events whose signatures originate from $t\bar{t}Z$ production. In this talk we
review two studies that represent the state of the art of theoretical modeling
of $t\bar{t}Z$ production by either performing the NLO QCD calculation of the
fully decayed $pp\rightarrow e^+\nu_e\mu^-\bar{\nu}_\mu b\bar{b}\tau^+\tau^-$
process (see Ref. [1]) or matching the NLO QCD calculation of $pp\rightarrow
t\bar{t}\ell^+\ell^-$ to parton shower, including top-quark decays with
approximate LO spin correlation (see Ref.[2]).
