  Quantum integrable models that possess $N=2$ supersymmetry are investigated
on the half-space. Conformal perturbation theory is used to identify some $N=2$
supersymmetric boundary integrable models, and the effective boundary
Landau-Ginzburg formulations are constructed. It is found that $N=2$
supersymmetry largely determines the boundary action in terms of the bulk, and
in particular, the boundary bosonic potential is $|W|^2$, where $W$ is the bulk
superpotential. Supersymmetry is also investigated using the affine quantum
group symmetry of exact scattering matrices, and the affine quantum group
symmetry of boundary reflection matrices is analyzed both for supersymmetric
and more general models. Some $N=2$ supersymmetry preserving boundary
reflection matrices are given, and their connection with the boundary
Landau-Ginzburg actions is discussed.
