Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking or media memorability. In this article, we systematically review different types of instance ranking problems, i.e., ranking problems that require the prediction of an order of the response variables, and the corresponding loss functions resp. goodness criteria. We discuss the difficulties when trying to optimize those criteria. As for a detailed and comprehensive overview of existing machine learning techniques to solve such ranking problems, we systemize existing techniques and recapitulate the corresponding optimization problems in a unified notation. We also discuss to which of the ranking problems the respective algorithms are tailored and identify their strengths and limitations. Computational aspects and open research problems are also considered.