  We present the Standard Model Effective Field Theories (SMEFT) from purely
on-shell arguments. Starting from a few basic assumptions such as Poincar\'e
invariance and locality, we classify all the renormalisable and
non-renormalisable interactions at the lowest order in the couplings. From
these building blocks, we review how locality and unitarity enforce Lie algebra
structures to appear in the S-matrix elements together with relations among
couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm
to compute any higher-point tree-level amplitude (or form factor) in generic
EFTs, bypassing BCFW-like recursion relations which are known to be problematic
when non-renormalisable interactions are involved. Finally, using known
amplitudes techniques we compute the mixing matrix of SMEFT irrelevant
interactions up to mass dimension 8, to linear order in the effective
interactions.
