The present review aims to summarize the main research findings, in the last four decades, on the Squeeze Film Damper (SFD) and its application. In this first part, a survey of the construction characteristics and operating features of the SFD, as a separate component, is reported, as inferred from the technical literature consulted, through a number of theoretical approaches and experimental results. Part II of the paper will review research work on the dynamic behavior of rotors on supports equipped with SFDs.