  Since Buchberger's initial algorithm for computing Gr\"obner bases in 1965
many attempts have been taken to detect zero reductions in advance.
Buchberger's Product and Chain criteria may be known the most, especially in
the installaton of Gebauer and M\"oller. A relatively new approach are
signature-based criteria which were first used in Faug\`ere's F5 algorithm in
2002. For regular input sequences these criteria are known to compute no zero
reduction at all. In this paper we give a detailed discussion on zero
reductions and the corresponding syzygies. We explain how the different methods
to predict them compare to each other and show advantages and drawbacks in
theory and practice. With this a new insight into algebraic structures
underlying Gr\"obner bases and their computations might be achieved.
