In this survey, we discuss the task of automatically classifying medical documents into the taxonomy of the International Classification of Diseases (ICD), by the use of deep neural networks. The literature in this domain covers different techniques. We will assess and compare the performance of those techniques in various settings and investigate which combination leverages the best results. Furthermore, we introduce an hierarchical component that exploits the knowledge of the ICD taxonomy. All methods and their combinations are evaluated on two publicly available datasets that represent ICD-9 and ICD-10 coding, respectively. The evaluation leads to a discussion of the advantages and disadvantages of the models.