  We review the status of calculations in the Standard Model Effective Field
Theory (SMEFT) beyond leading order (LO). Improving the SMEFT beyond LO allows
theoretical errors to be characterized and reduced when considering SMEFT
interpretations of the data, which is essential considering the improving
experimental precision at LHC. Next to leading order results also allow a more
consistent analysis of measurements with different effective scales in the
SMEFT. Going beyond LO is clearly important in the event that deviations from
the SM are large enough that experimental indications of physics beyond the SM
emerge. We discuss a consistent and well defined approach to LO in the SMEFT,
so that the improvement to NLO is straightforward. We discuss the basic issues
involved in improving calculations to NLO in the SMEFT, and review the advances
in this direction that have been achieved to date.
