Modern Astrophysics is one of the most data intensive research fields in the world and is driving many of the required innovations in the 'big data' space. Foremost in astronomy in terms of data generation is radio astronomy, and in the last decade an increase in global interest and investment in the field had led to a large number of new or upgraded facilities which are each currently generating petabytes of data per annum. The peak of this so-called 'radio renaissance' will be the Square Kilometre Array (SKA) - a global observatory designed to uncover the mysteries of the Universe. The SKA will create the highest resolution, fastest frame rate movie of the evolving Universe ever and in doing so will generate 160 terrabytes of data a day, or close to 5 zettabytes of data per annum. Furthermore, due to the extreme faintness of extraterrestrial radio signals, the telescope elements for the SKA must be located in radio quite parts of the world with very low population density. Thus the project aims to build the most data intensive scientific experiment ever, in some of the most remote places on Earth. Generating and serving scientific data products of this scale to a global community of researchers from remote locations is just the first of the 'big data' challenges the project faces. Coordination of a global network of tiered data resources will be required along with software tools to exploit the vast sea of results generated. In fact, to fully realize the enormous scientific potential of this project, we will need not only better data distribution and coordination mechanisms, but also improved algorithms, artificial intelligence and ontologies to extract knowledge in an automated way at a scale not yet attempted in science. In this keynote I will present an overview of the SKA project, outline the 'big data' challenges the project faces and discuss some of the approaches we are taking to tame the astronomical data deluge we face.