  We introduce a generalization of the original Coordinate Bethe Ansatz that
allows to treat the case of open spin chains with non-diagonal boundary
matrices. We illustrate it on two cases: the XXX and XXZ chains.
  Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see
arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.
