An informal introduction to our recent work on the principal chiral model
with boundary. We found that both classically integrable boundary conditions
and quantum boundary S-matrices were classified by the symmetric spaces G/H.
The connection is explained by the presence of a twisted Yangian algebra of
non-local charges.Comment: Updated v2 based on talk at 'IFTs, Solitons and Duality', Sao Paulo
2002; v1 appeared in Proc. QGIS Prague 200