The Square Kilometre Array (SKA) is an international project to build and operate the most powerful radio telescope ever conceived, in order to answer a range of fundamental questions in cosmology and astrophysics. The SKA will be a facility built in two phases, primarily in two host countries (Australia and South Africa), and in four technology elements (telescope systems). In this paper I briefly outline the science goals and technical challenges of the SKA. I will focus most attention on the Big Data signal processing challenges of the SKA, highlighting the need for the astronomy community to reach out into other disciplines such as the broad signal processing community, in order to obtain fresh and interdisciplinary perspectives on these challenges.