  Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is
formulated in terms of eigenvalue relations for monodromy matrix operators. The
Quantum Inverse Scattering Method provides the appropriate tools to treat the
extended symmetry and to recover as its consequences many known features like
cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction,
Grassmannian integral representation, $\mathrm{R}$-invariants and on-shell
diagram approach.
