Talk:Buchberger's algorithm
The remark that Buchberger's algorithm is (not considering any refinements thereof) the only known way to compute Groebner bases is not correct.
Another approach that has been implemented (and that has been found to be very competitive in terms of running time) is based on the concept of involutive bases. The latter are based on ideas from differential algebra, in particular on work from the french mathematician Riquier. Involutive bases have been investigated, among others, by Gerdt and Blinkov.