For a dynamical system, to be non-statistical means that as the time tends to infinity, the dynamics does not shows convergent statistical behavior in the sense of Birkhoff averages. In this lecture, first we introduce some examples of this kind of behavior in different family of dynamics. Next, we explain the connection between this dynamical behavior and another one called "statistical instability", and show that in any family of dynamical systems, the existence of a "large" set of statistically unstable maps, implies the existence of non-statistical ones. And finally, we present a consequence of this fact for the family of maps that a priori we know they do not display non-statistical behavior, e.g. conservative maps.