Efforts have been recently made to construct ontologies for network security. The proposed ontologies are related to specific aspects of network security. Therefore, it is necessary to identify the specific aspects covered by existing ontologies for network security. A review and analysis of the principal issues, challenges, and the extent of progress related to distinct ontologies was performed. Each example was classified according to the typology of the ontologies for network security. Some aspects include identifying threats, intrusion detection systems (IDS), alerts, attacks, countermeasures, security policies, and network management tools. The research performed here proposes the use of three stages: 1. Inputs; 2. Processing; and 3. Outputs. The analysis resulted in the introduction of new challenges and aspects that may be used as the basis for future research. One major issue that was discovered identifies the need to develop new ontologies that relate to distinct aspects of network security, thereby facilitating management tasks.