Due to the rising dependency on digital technology, cybersecurity has emerged as a more prominent field of research and application that typically focuses on securing devices, networks, systems, data and other resources from various cyber-attacks, threats, risks, damages, or unauthorized access. Artificial Intelligence (AI), also referred to as a crucial technology of the current Fourth Industrial Revolution (Industry 4.0 or 4IR), could be the key to intelligently dealing with these cyber issues. Various forms of AI methodologies, such as analytical, functional, interactive, textual as well as visual AI can be employed to get the desired cyber solutions according to their computational capabilities. However, the dynamic nature and complexity of real-world situations and data gathered from various cyber sources make it challenging nowadays to build an effective AI-based security model. Moreover, defending robustly against adversarial attacks is still an open question in the area. In this paper, we provide a comprehensive view on "Cybersecurity Intelligence and Robustness", emphasizing multi-aspects AI-based modeling and adversarial learning that could lead to addressing diverse issues in various cyber applications areas such as detecting malware or intrusions, zero-day attacks, phishing, data breach, cyberbullying and other cybercrimes. Thus the eventual security modeling process could be automated, intelligent, and robust compared to traditional security systems. We also emphasize and draw attention to the future aspects of cybersecurity intelligence and robustness along with the research direction within the context of our study. Overall, our goal is not only to explore AI-based modeling and pertinent methodologies but also to focus on the resulting model's applicability for securing our digital systems and society.