While we are witnessing rapid growth in data across the sciences and in many applications, this growth is particularly remarkable in the medical domain, be it because of higher resolution instruments and diagnostic tools (e.g. MRI), new sources of structured data like activity trackers, the wide-spread use of electronic health records and many others. The sheer volume of the data is not, however, the only challenge to be faced when using medical data for research. Other crucial challenges include data heterogeneity, data quality, data privacy and so on. In this article, we review solutions addressing these challenges by discussing the current state of the art in the areas of data integration, data cleaning, data privacy, scalable data access and processing in the context of medical data. The techniques and tools we present will give practitioners — computer scientists and medical researchers alike — a starting point to understand the challenges and solutions and ultimately to analyse medical data and gain better and quicker insights.