  In this PhD thesis we extend the twistor formalism to encompass (partially)
off-shell quantities. We describe all gauge-invariant local composite operators
in twistor space and show that they immediately generate all tree-level form
factors of the MHV type. We use the formalism to compute form factors at NMHV
and higher NkMHV level in parallel to how this had been done for amplitudes
previously. Finally, we move on to integrability by computing the one-loop
dilatation operator in the scalar sector of the theory in twistor space.
