Algorithms in computational $D$-module theory are discussed. Especially new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions are considered. A new method to compute the Bernstein-Sato polynomial is introduced. All algorithms considered in the paper have been implemented in {\sc Singular}. The implementation is discussed and examples are given.
Reviewer: Gerhard Pfister (Kaiserslautern)