  In this contribution to the Snowmass 2021 process we review theoretical
developments in the Standard Model Effective Field Theory (SMEFT) with a focus
on effects at the dimension-8 level and beyond. We review the theoretical
advances that led to the complete construction of the operator bases for the
dimension-8 and dimension-9 SMEFT Lagrangians. We discuss the possibility of
obtaining all-orders results in the $1/\Lambda$ expansion for certain SMEFT
observables as well as the current status of renormalization group running and
implications for positivity, and briefly present the on-shell approach to
constructing SMEFT amplitudes. Finally we present several new phenomenological
effects that first arise at dimension-8 and discuss the impact of these terms
on experimental analyses.
