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Big data holds great promises and opportunities for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. Huge size and high dimensionality of big data introduce various statistical, computational, legal and privacy challenges. These challenges are distinguished and formidable, and require new statistical, computational and legal paradigm. In this paper, we present a brief non-technical overview of the salient features of big and high dimensional data; explain how these features impact on paradigm changes on statistical, computational and legal aspects. The paper ends with some concluding remarks about these new challenges and future research directions.