In this article we describe properties of unbounded operators related to evolutionary problems. It is a survey article which also contains several new results. For instance we give a characterization of cosine functions in terms of mild well-posedness of the Cauchy problem of order 2, and we show that the property of having a bounded $H^{\infty }$-calculus is stable under rank-1 perturbations whereas the property of being associated with a closed form and the property of generating a cosine function are not....