Cognitive technologies give us the ability to ingest data from millions of disparate information sources to identify actionable threat intelligence that is meaningful to social networks, allowing them to prepare proactively. The confidentiality of big data is usually the main focus, thus making encryption and access control techniques the research areas when it comes to big data security. In this paper, we investigated the state on cybersecurity in big data. We also addressed the role of cognitive technologies and artificial intelligence in cybersecurity areas, and some of the challenges cognitive modeling has to overcome before it becomes an important feature in the cybersecurity toolkit. Furthermore, we present future trends in cognitive technologies on cybersecurity in Big Data that we foresee, and the challenges associated with it.