Weglein, A.B., Stolt, R.H. and Mayhan, J.D., 2011. Reverse time migration and Green’s theorem: Part I - the evolution of concepts, and setting the stage for the new RTM method. Journal of Seismic Exploration, 20: 73-90. In this paper, part I of a two paper set, we describe the evolution of Green’s theorem based concepts and methods for downward continuation and migration. This forms the foundation and context for developing Green’s theorem reverse time migration (RTM), in part II. We present the evolution of seismic exploration wave-field prediction models, as steps towards more completeness, consistency, realism and predictive effectiveness. Using simple and accessible analytic examples, we describe the difference between the need for subsurface information when the goal is a structure map, and contrast that with the case when the goal is both an accurate depth image and subsequent amplitude analysis at depth, that is, between migration and migration-inversion. The relationship between Green’s theorem and the Lippmann Schwinger equation of scattering theory is used to help define the need behind the evolution of Green’s theorem concepts and developments in seismic imaging, as well as to provide a new insight for classic results like, e.g., the Sommerfeld radiation condition. This paper provides a platform and detailed background for the second of this two paper set, where part II provides a new and consistent theory and method for RTM.