The underlying paradigm of big data-driven machine learning reflects the desire of deriving better conclusions from simply analyzing more data, without the necessity of looking at theory and models. Is having simply more data always helpful? In 1936, The Literary Digest collected 2.3M filled in questionnaires to predict the outcome of that year's US presidential election. The outcome of this big data prediction proved to be entirely wrong, whereas George Gallup only needed 3K handpicked people to make an accurate prediction. Generally, biases occur in machine learning whenever the distributions of training set and test set are different. In this work, we provide a review of different sorts of biases in (big) data sets in machine learning. We provide definitions and discussions of the most commonly appearing biases in machine learning: class imbalance and covariate shift. We also show how these biases can be quantified and corrected. This work is an introductory text for both researchers and practitioners to become more aware of this topic and thus to derive more reliable models for their learning problems.