  We describe the twisted Yangians Y(g,h) which arise as boundary remnants of
Yangians Y(g) in 1+1D integrable field theories. We describe and extend our
recent construction of the intertwiners of their representations (the rational
boundary S- or 'K'-matrices) and perform a case-by-case analysis for all pairs
(g,h), giving the h-decomposition of Y(g,h)-representations where possible.
