This article reviews the application of several IP rights (copyright, patent, sui generis database right, data exclusivity and trade secret) to Big Data. Beyond the protection of software used to collect and process Big Data corpora, copyright’s traditional role is challenged by the relatively unstructured nature of the non-relational (noSQL) databases typical of Big Data corpora. This also impacts the application of the EU sui generis right in databases. Misappropriation (tort-based) or anti-parasitic behaviour protection might apply, where available, to data generated by AI systems that has high but short-lived value. Copyright in material contained in Big Data corpora must also be considered. Exceptions for Text and Data Mining (TDM) are already in place in a number of legal systems and likely to emerge to allow the creation and use of corpora of literary and artistic works, such as texts and images. In the patent field, AI systems using Big Data corpora of patents and scientific literature can be used to expand patent applications. They can also be used to “guess” and disclose future incremental innovation. These developments pose serious doctrinal and normative challenges to the patent system and the incentives it creates in a number of areas, though data exclusivity regimes can fill certain gaps in patent protection for pharmaceutical and chemical products. Finally, trade secret law, in combination with contracts and technological protection measures, can protect data corpora and sets of correlations and insights generated by AI systems.