Recent observations have shown that the Universe is dominated by two mysterious components, Dark Matter and Dark Energy. Their nature pose some of the most pressing questions in fundamental physics today.Weak gravitational lensing, or 'cosmic' shear', is a powerful technique to probe these dark components. We will first review the principles of cosmic shear and its current observational status. We will describe the future surveys which will be available for cosmic shear studies. We will then highlight key challenges in data analysis which need to be met for the potential of these future surveys to be fully realised.