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This paper reviews the most important information fusion data-driven algorithms based on Machine Learning (ML) techniques for problems in Earth observation. Nowadays we observe and model the Earth with a wealth of observations, from a plethora of different sensors, measuring states, fluxes, processes and variables, at unprecedented spatial and temporal resolutions. Earth observation is well equipped with remote sensing systems, mounted on satellites and airborne platforms, but it also involves in-situ observations, numerical models and social media data streams, among other data sources. Data-driven approaches, and ML techniques in particular, are the natural choice to extract significant information from this data deluge. This paper produces a thorough review of the latest work on information fusion for Earth observation, with a practical intention, not only focusing on describing the most relevant previous works in the field, but also the most important Earth observation applications where ML information fusion has obtained significant results. We also review some of the most currently used data sets, models and sources for Earth observation problems, describing their importance and how to obtain the data when needed. Finally, we illustrate the application of ML data fusion with a representative set of case studies, as well as we discuss and outlook the near future of the field.