  We describe how Groebner bases can be used to solve the reduction problem for
Feynman integrals, i.e. to construct an algorithm that provides the possibility
to express a Feynman integral of a given family as a linear combination of some
master integrals. Our approach is based on a generalized Buchberger algorithm
for constructing Groebner-type bases associated with polynomials of shift
operators. We illustrate it through various examples of reduction problems for
families of one- and two-loop Feynman integrals. We also solve the reduction
problem for a family of integrals contributing to the three-loop static quark
potential.
