This paper reviews the impact of data science and artificial intelligence (AI) on future ‘datadriven’ insurance markets. The impact of insurance automation (driven by so-called Black Swan1 events such as Covid-19) mirrors the impact of algorithmic trading that changed radically the capital markets (Koshiyama et al., 2020). The data science technologies driving change include: Big data, AI analytics, Internet of Things, and Blockchain technologies. These technologies are important since they underpin the automation of the insurance markets and risk analysis, and provide the context for the algorithms, such as AI machine learning and computational statistics, which provide powerful analytics capabilities. New AI algorithms are constantly emerging, with each ‘strain’ mimicking a new form of human learning, reasoning, knowledge, and decision-making. The current main disrupting forms of learning include deep learning, adversarial learning, federated learning, transfer and meta learning. Albeit these modes of learning have been in the AI/ML field more than a decade, they are now more applicable due to the availability of data, computing power and infrastructure. These forms of learning have produced new models (e.g., long short-term memory, generative adversarial networks) and leverage important applications (e.g., Natural Language Processing, Adversarial Examples, Deep Fakes, etc.). These new models and applications will drive changes in future insurance markets, so it is important to understand their computational strengths and weaknesses. The contribution of this paper is to review the data science technologies and specifically AI algorithms, their computational strengths and weaknesses, and discuss their future impact on the insurance markets.