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 K¯NN\documentclass[12pt]{minimal}
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\begin{document}$$\bar{K}NN$$\end{document} and K¯K¯N\documentclass[12pt]{minimal}
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\begin{document}$$\bar{K}\bar{K}N$$\end{document} systems are considered. In particular, quasi-bound states in K-pp\documentclass[12pt]{minimal}
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\begin{document}$$K^- pp$$\end{document} and K-K-p\documentclass[12pt]{minimal}
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\begin{document}$$K^- K^- p$$\end{document} systems were investigated together with antikaonic deuterium atom. Near-threshold scattering of antikaons on deuteron, including the K-d\documentclass[12pt]{minimal}
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\begin{document}$$K^- d$$\end{document} 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 K¯N\documentclass[12pt]{minimal}
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\begin{document}$$\bar{K}N$$\end{document}, ΣN\documentclass[12pt]{minimal}
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\begin{document}$${\varSigma }N$$\end{document}, K¯K¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{K}\bar{K}$$\end{document}, 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.
