One of the mathematical definitions of "chaos" is given in terms of the measure-theoretic (or metric, or Kolmogorov) entropy, and chaotic dynamical systems are often defined to be systems with positive entropy. However many systems with a "chaotic" behaviour have zero entropy, and the same is true for some time series of the real world. In this talk I will first introduce the notion of zero entropy systems and some examples. Then I will show how these systems represent an interesting challenge from the mathematical point of view, as many results from Dynamical Systems Theory do not hold, and some definitions are hard to be extended to these systems.