  The paper contains a review of the exact or accurate results achieved in the
field of the three-body antikaon-nucleon physics. Different states and
processes in $\bar{K}NN$ and $\bar{K}\bar{K}N$ systems are considered. In
particular, quasi-bound states in $K^- pp$ and $K^- K^- p$ systems were
investigated together with antikaonic deuterium atom. Near-threshold scattering
of antikaons on deuteron, including the $K^- d$ scattering length, and
applications of the scattering amplitudes are also discussed.
  All exact three-body results were calculated using some form of Faddeev
equations. Different versions of $\bar{K}N$, $\Sigma N$, $\bar{K}\bar{K}$, and
$NN$ potentials, specially constructed for the calculations, allowed
investigation of the dependence of the three-body results on the two-body
input. Special attention is paid to the antikaon-nucleon interaction, being the
most important for the three-body systems. Approximate calculations, performed
additionally to the exact ones, demonstrate accuracy of the commonly used
approaches.
