Most of the classic theoretical systems and tools in statistics, data mining and machine learning are built on the fundamental assumption of IIDness, which assumes the independence and identical distribution of underlying objects, attributes and/or values. However, complex behavioral and social problems often exhibit strong couplings and heterogeneity between values, attributes and objects (i.e., non-IIDness). This fundamentally challenges the IIDness-based learning methodologies and techniques. This paper presents a high-level overview of the needs, challenges and opportunities of non-IIDness learning for handling complex behavioral and social problems. By reviewing the nature and issues of classic IIDness-based algorithms in frequent pattern mining, clustering and classification to complex behavioral and social applications, concepts, structures, frameworks and exemplartechniquesarediscussedfornon-IIDnesslearning.Casestudies,relatedworkandprospects of non-IIDness learning are presented. Non-IIDness learning is also a fundamental issue in big data analytics.