Ward identities of SUSY and R-symmetry relate n -point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn1.gif] {{\cal N}=4} SYM and ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn2.gif] {{\cal N}=8} supergravity. The solution, valid at both tree and loop level, expresses any N K MHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn3.gif] {{\cal N}} _ K Young diagrams. The SUSY Ward identities also impose constraints on the matrix elements of candidate ultraviolet counterterms in ##IMG## [http://ej.iop.org/images/1751-8121/44/45/454009/jpa389327ieqn4.gif] {{\cal N}=8} supergravity, and they can be studied using superamplitude basis expansions. This leads to a novel and quite comprehensive matrix element approach to counterterms, which we also review.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90831/1/1751-8121_44_45_454009.pd
