The paper can be considered as a review, in which - on the basis of certain assumptions - a unified approach to abstract linear nonautonomous parabolic equations is proposed. In particular, the linear parabolic Cauchy problem
is studied in a Banach space E, with and f:[0,T] as prescribed data. In (1) A(t) is a family of closed linear operators in E which are generators of analytic semigroups, and whose domain may change with t and be not dense in E. Existence, uniqueness and regularity results are illustrated. The paper consists of 7 sections, rich in definitions, lemmas, propositions and theorems. In the last section examples and comparisons with the available literature are discussed.