We discuss no-go theorems that once forbid the existence of massless higher-spin theories in flat space and how to avoid them using chiral field representation (a representation that has deep roots in twistor theory). With this representation, one can construct some examples of twistorial higher-spin theories that surpass all the obstacles of no-go theorems with the price of giving up parity invariance.
We then discuss the recent development of a higher-spin gauge theory induced by the IKKT matrix model (HS-IKKT), where higher-spin fields are naturally introduced to mitigate the effect of local Lorentz-violation. This part of the talk will focus on the spinorial formalism of HS-IKKT theory.