Real world datasets are often accompanied with various types of anomalous or exceptional entries which are often referred to as outliers. Detecting outliers and distinguishing noise form true exceptions is important for effective data mining. This chapter presents two methods for outlier detection and analysis using the self-organizing map (SOM), where one is more suitable for categorical and the other for continuous data. They are generally based on filtering out the instances which are not captured by or are contradictory to the obtained concept hierarchy for the domain. We demonstrate how the dimension of the output space plays an important role in the kind of patterns that will be detected as outlying. Furthermore, the concept hierarchy itself provides extra criteria for distinguishing noise from true exceptions. The effectiveness of the proposed outlier detection and analysis strategy is demonstrated through the experiments on publicly available real world datasets.