The main objective of this talk is to discuss both deterministic and statistical aspects of inverse problems in subsurface flow models. In the first part of my talk I discuss the potential lack of accuracy and robustness of typical approaches for parameter identification in subsurface flow models. I then describe iterative regularisation methods that can be applied to overcome the aforementioned limitations of the standard approach. In addition, inspired by ideas from iterative regularisation, I propose ensemble methods that aim at providing a statistical description of the inverse problem. In particular, a regularising ensemble Kalman method is proposed as a derivative-free iterative regularisation method. These ensemble methods quantify the uncertainty in the unknown parameters of the subsurface. Towards the end of my talk some numerical experiments are displayed to show the capabilities of the methods under consideration.