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While recommendation plays an increasingly critical role in our living, study, work, and entertainment, the recommendations we receive are often for irrelevant, duplicate, or uninteresting products and services. A critical reason for such bad recommendations lies in the intrinsic assumption that recommended users and items are independent and identically distributed (IID) in existing theories and systems. Another phenomenon is that, while tremendous efforts have been made to model specific aspects of users or items, the overall user and item characteristics and their non-IIDness have been overlooked. In this paper, the non-IID nature and characteristics of recommendation are discussed, followed by the non-IID theoretical framework in order to build a deep and comprehensive understanding of the intrinsic nature of recommendation problems, from the perspective of both couplings and heterogeneity. This non-IID recommendation research triggers the paradigm shift from IID to non-IID recommendation research and can hopefully deliver informed, relevant, personalized, and actionable recommendations. It creates exciting new directions and fundamental solutions to address various complexities including cold-start, sparse data-based, cross-domain, group-based, and shilling attack-related issues.