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When a sample is taken from a population additionally for a certain of its components called domains also estimates are needed for certain parameters. When domain-wise samples are too small these estimates turn out poor in efficiency. By borrowing strength from other domains how data may be appropriately used is an important issue. How to settle this using domain as well as past data is a story related in this monograph. For this appropriate model-assisted analysis is described in details. Historical developments are narrated and live data-base emperical findings are presented in great details. Mainly the author's own research in collaboration with his students and colleagues is stressed. Contemporary research by others is also touched to the extent possible in this short output. Further a point of interest is to start with classical estimation methods based on unequal probability sampling and to follow up with appropriate modelling. This has been diligently implemented as is notusually emphasised in the current literature on Small Area Estimation.