In this talk, I will explore to what extent generic scattering amplitudes can be built using a purely algebraic language which builds on the spinor-helicity
formalism. It is well-known that simply enforcing two constraints (Lorentz covariance and consistent factorisation over intermediate on-shell states) which
are strictly physical in nature, leads to a huge restriction on the number of viable theories. I will re-derive some known results in an algebraic language,
and argue how this description lends itself to the manipulation and simplification of amplitudes, and naturally highlights the connection of "amplitudeology"
with different topics such as the infrared structure of field theories and effective field theory.