S-bases as a tool to solve reduction problems for Feynman integrals

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Gröbner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.