Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the concept of collapsibility deals with dimension-reduction aspects, when Simpson's paradox does not occur. We discuss in this paper in some detail the nature and the genesis of Simpson's paradox with respect to well-known examples and also various concepts of collapsiblity. The main aim is to bring out the close connections between these two phenomena, especially with regard to the analysis of contingency tables, regression models and a certain measure of association or a dependence function. There is a vast literature on these topics and so we focus only on certain aspects, recent developments and some important results in the above-mentioned areas.