The paper describes the use of adaptive and non-periodic sampling in different fields of System Theory and Control. The review is organized in a very comprehensive way and it presents results of the last thirty years about the problem of signal applications using as main tool adaptive sampling schemes including results is the improvement of the transient behaviors. Also, related results are presented about the use of non-periodic sampling in compensation as an alternative design to the well-known frequency domain methods and about the choice of the sampling points in order to improve the transmission of measuring and/or rounding errors towards the results when studying the properties of dynamic systems such as controllability, observability and identifiability.