Cybersecurity is a fast-evolving discipline that is always in the news over the last decade, as the number of threats rises and cybercriminals constantly endeavor to stay a step ahead of law enforcement. Over the years, although the original motives for carrying out cyberattacks largely remain unchanged, cybercriminals have become increasingly sophisticated with their techniques. Traditional cybersecurity solutions are becoming inadequate at detecting and mitigating emerging cyberattacks. Advances in cryptographic and Artificial Intelligence (AI) techniques (in particular, machine learning and deep learning) show promise in enabling cybersecurity experts to counter the ever-evolving threat posed by adversaries. Here, we explore AI's potential in improving cybersecurity solutions, by identifying both its strengths and weaknesses. We also discuss future research opportunities associated with the development of AI techniques in the cybersecurity field across a range of application domains.