"Practical Computations with Gr\"obner Bases" Daniel Lichtblau Wolfram Research, Incorporated 100 Trade Centre Dr. Champaign, IL, 61820 USA E-mail:danl@wolfram.com Gr\"obner bases have become a pervasive tool in computational mathematics. In this paper we show several sorts of Gr\"obner basis computations in Mathematica. We discuss computations of approximate Gr\"obner bases, with applications to solving systems and implicitization. We also show how to use the built-in GroebnerBasis function to compute polynomial greatest-common-divisors over various fields, series inverses, syzygy modules, and more. Much of this is by now classical; the emphasis is not on new results but rather on effective use of off-the-shelf technology. We will point out areas where existing functionality needs enhancement, and note some directions for future work.