We present a generalization the G. Letzter's theory of quantum symmetric
pairs of semisimple Lie algebras for the case of quantum affine algebras. We
then study solutions of the reflection equation for the quantum affine algebras
sl(2) and gl(1|1) and their Yangian limit for singlet (diagonal) and vector
(non-diagonal) boundary conditions. We construct the corresponding quantum
affine coideal subalgebras that are based on the quantum symmetric pairs, and
the (generalized) twisted Yangians.Comment: 31 page; v2: updated versio