Zero-range hamiltonians for three quantum particles

Characterisation of the confined states of quantum systems made of many particles interacting via short range forces was the main goal for theoretical physicists investigating the structure of nuclei in the early years of Quantum Mechanics. A rigorous formulation of the problem was given at the beginning of the sixties by the Russian school of mathematical physics. The analysis of the three-body problem already revealed intriguing pathologies opening at the same time promising prospects for the future. We summarise the history and recent attempts of this line of research.