In this talk I will discuss how Gröbner bases can be used to perform integration-by-parts (IBP) reductions of loop integrals. After an introduction to IBP reduction, Gröbner bases, and other notions from algebraic geometry, I will show several examples where the Gröbner bases approach can be successfully applied to the loop-integral reduction. I will also discuss current limitations of the approach and how they can be partially circumvented by an ansatz based on linear algebra.