Her research considers algebraic geometry. She has developed the mathematical theories that underpin algebraic stacks. Stacks were first introduced to understand the moduli space of curves.
In 2018, Fantechi received the Prof. Luigi Tartufari award from the Accademia deiLincei. She was awarded the MSRI Chancellor's Professorship for 2017-2018, and spent a year at the University of California, Berkeley. In 2022, Fantechi was the first woman mathematician to become a member of the Accademia dei Lincei.