  We apply on-shell methods to the bottom-up construction of electroweak
amplitudes, allowing for both renormalizable and non-renormalizable
interactions. We use the little-group covariant massive-spinor formalism, and
flesh out some of its details along the way. Thanks to the compact form of the
resulting amplitudes, many of their properties, and in particular the
constraints of perturbative unitarity, are easily seen in this formalism. Our
approach is purely bottom-up, assuming just the standard-model electroweak
spectrum as well as the conservation of electric charge and fermion number. The
most general massive three-point amplitudes consistent with these symmetries
are derived and studied in detail, as the primary building blocks for the
construction of scattering amplitudes. We employ a simple argument, based on
tree-level unitarity of four-point amplitudes, to identify the three-point
amplitudes that are non-renormalizable at tree level. This bottom-up analysis
remarkably reproduces many low-energy relations implied by electroweak symmetry
through the standard-model Higgs mechanism and beyond it. We then discuss
four-point amplitudes. The gluing of three-point amplitudes into four-point
amplitudes in the massive spinor helicity formalism is clarified. As an
example, we work out the $\psi^c \psi Zh$ amplitude, including also the
non-factorizable part. The latter is an all-order expression in the
effective-field-theory expansion. Further constraints on the couplings are
obtained by requiring perturbative unitarity. In the $\psi^c \psi Zh$ example,
one for instance obtains the renormalizable-level relations between vector and
fermion masses and gauge and Yukawa couplings. We supplement our bottom-up
derivations with a matching of three- and four-point amplitude coefficients
onto the standard-model effective field theory (SMEFT) in the broken
electroweak phase.
