Hierarchical Self-Organizing Networks are used to reveal the topology and structure of datasets. These methodologies create crisp partitions of the dataset producing tree structures composed of prototype vectors, permitting the extraction of a simple and compact representation of a dataset. However, in many cases observations could be represented by several prototypes with certain degree of membership. Nevertheless, crisp partitions are forced to classify observations in just one group, losing information about the real dataset structure. To deal with this challenge we propose Fuzzy Growing Hierarchical Self-Organizing Networks (FGHSON). FGHSON are adaptive networks which are able to reflect the underlying structure of the dataset in a hierarchical fuzzy way. These networks grow by using three parameters which govern the membership degree of data observations to the prototype vectors and the quality of the hierarchical representation. However, different combinations of values of these parameters can generate diverse networks. This chapter explores how these combinations affect the topology of the network and the quality of the prototypes; in addition the motivation and the theoretical basis of the algorithm are presented.