  We present theoretical calculations of total cross sections and top-quark
transverse-momentum and rapidity distributions in the associated production of
a top-antitop pair with a photon ($t{\bar t}\gamma$ production). We include
complete QCD and electroweak corrections at NLO as well as soft-gluon
corrections at approximate NNLO (aNNLO). The aNNLO corrections are very
significant, they decrease theoretical uncertainties, and they are needed for
better comparison with data from the LHC.
