In view of no direct sign of new physics so far and the pending
puzzles that cannot be solved within the Standard Model (SM) the Higgs
sector plays an increasingly important role as a portal to physics
beyond the SM. New physics can be parametrized in a rather
model-independent way in the SM effective theory (SMEFT). In this
contribution I will discuss what we can learn about new physics from
Higgs fits to SMEFT higher-dimensional operators.