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This paper provides a review on machine learning methods applied to the asset management discipline. Firstly, we describe the theoretical background of both machine learning and finance that will be needed to understand the reviewed methods. Next, the main datasets and sources of data are exposed to help researchers decide which are the best ones to suit their targets. After that, the existing methods are reviewed, highlighting their contribution and significance in the analyzed financial disciplines. Furthermore, we also describe the most common performance criteria that are applied to compare such methods quantitatively. Finally, we carry out a critical analysis to discuss the current state-of-the-art and lay down a set of future research directions. This research has been funded by Faculty of Economics and Business Administration (ICADE), Universidad Pontificia Comillas.