“Solving Scattering in N=4 Super-Yang-Mills Theory” is the latest review of progress with amplitudes. The “antipodal duality” is the biggest new mystery there.
Also, a reminder that the correct ontology of this theory should also be the correct ontology of string theory, because of AdS/CFT: studying subtle changes in the operator algebra of the theory, in phases dual to an AdS black hole.
N=4 Super-Yang-Mills Theory 
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