  A self-consistent exposition of the theory of tree-level superamplitudes of
the 4d N=4 and 6d N=(1,1) maximally supersymmetric Yang-Mills theories is
provided. In 4d we work in non-chiral superspace and construct the
superconformal and dual superconformal symmetry generators of the N=4 SYM
theory using the non-chiral BCFW recursion to prove the latter. In 6d we
provide a complete derivation of the standard and hidden symmetries of the
tree-level superamplitudes of N=(1,1) SYM theory, again using the BCFW
recursion to prove the dual conformal symmetry. Furthermore, we demonstrate
that compact analytical formulae for tree-superamplitudes in N=(1,1) SYM can be
obtained from a numerical implementation of the supersymmetric BCFW recursion
relation. We derive compact manifestly dual conformal representations of the
five- and six-point superamplitudes as well as arbitrary multiplicity formulae
valid for certain classes of superamplitudes related to
ultra-helicity-violating massive amplitudes in 4d. We study massive tree
superamplitudes on the Coulomb branch of the N=4 SYM theory from dimensional
reduction of the massless superamplitudes of the six-dimensional N=(1,1) SYM
theory. We exploit this correspondence to construct the super-Poincare and
enhanced dual conformal symmetries of massive tree superamplitudes in N=4 SYM
theory which are shown to close into a finite dimensional algebra of Yangian
type. Finally, we address the fascinating possibility of uplifting massless 4d
superamplitudes to 6d massless superamplitudes proposed by Huang. We confirm
the uplift for multiplicities up to eight but show that finding the uplift is
highly non-trivial and in fact not of a practical use for multiplicities larger
than five.
