  This talk, based principally on arXiv:1103.0786, is devoted to properties of
tree-level S-matrices of N=2,4,8 SYM in D=2+1. We'll discuss an on-shell
formalism for three-dimensional theories inspired by the spinor-helicity
framework in four spacetime dimensions. Our framework will be shown be to
particularly well suited for the extraction of hidden symmetries and algebraic
structures that the scattering amplitudes of the three-dimensional theories
posses. In particular we shall discuss the manifest SO(N) symmetry of the
S-matrix to all orders in perturbation theory; a symmetry that the Lagrangians
of these theories do not have. After a brief discussion of the ramification of
the SO(N) invariance to the D2-M2 brane dualities, we shall introduce an
on-shell superfield framework for three-dimensional theories and end with a
surprising hint of the existence of non-local symmetries for the S-matrix of
the N=8 theory.
