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The importance of social security and social welfare business has been increasingly recognized in more and more countries. It impinges on a large proportion of the population and affects government service policies and people's life quality. Typical welfare countries, such as Australia and Canada, have accumulated a huge amount of social security and social welfare data. Emerging business issues such as fraudulent outlays, and customer service and performance improvements challenge existing policies, as well as techniques and systems including data matching and business intelligence reporting systems. The need for a deep understanding of customers and customer-government interactions through advanced data analytics has been increasingly recognized by the community at large. So far, however, no substantial work on the mining of social security and social welfare data has been reported. For the first time in data mining and machine learning, and to the best of our knowledge, this paper draws a comprehensive overall picture and summarizes the corresponding techniques and illustrations to analyze social security/welfare data, namely, social security data mining (SSDM), based on a thorough review of a large number of related references from the past half century. In particular, we introduce an SSDM framework, including business and research issues, social security/welfare services and data, as well as challenges, goals, and tasks in mining social security/welfare data. A summary of SSDM case studies is also presented with substantial citations that direct readers to more specific techniques and practices about SSDM.