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This paper advocates a problem-oriented approach for the design of artificial immune systems (AIS) for data mining. By problem-oriented approach we mean that, in real-world data mining applications the design of an AIS should take into account the characteristics of the data to be mined together with the application domain: the components of the AIS - such as its representation, affinity function, and immune process - should be tailored for the data and the application. This is in contrast with the majority of the literature, where a very generic AIS algorithm for data mining is developed and there is little or no concern in tailoring the components of the AIS for the data to be mined or the application domain. To support this problem-oriented approach, we provide an extensive critical review of the current literature on AIS for data mining, focusing on the data mining tasks of classification and anomaly detection. We discuss several important lessons to be taken from the natural immune system to design new AIS that are considerably more adaptive than current AIS. Finally, we conclude this paper with a summary of seven limitations of current AIS for data mining and ten suggested research directions.