Gamow states are vector states for the pure decaying part of a quantum resonance. We review and analyze the properties of Gamow vectors in different representations. In particular, we discuss the controversial problem of assigning a mean value of the energy for a Gamow state from several points of view. The question on whether a Gamow state is a pure state or not is also analyzed here, as has relevance on the assignation of a non-zero value for the entropy for (...) a Gamow state. (shrink)