Artificial Intelligence (AI) is a potentially powerful tool in the fight against the COVID- 19 pandemic. Since the outbreak of the pandemic, there has been a scramble to use AI. This article provides an early, and necessarily selective review, discussing the contribution of AI to the fight against COVID-19, as well as the current constraints on these contributions. Six areas where AI can contribute to the fight against COVID-19 are discussed, namely i) early warnings and alerts, ii) tracking and prediction, iii) data dashboards, iv) diagnosis and prognosis, v) treatments and cures, and vi) social control. It is concluded that AI has not yet been impactful against COVID-19. Its use is hampered by a lack of data, and by too much data. Overcoming these constraints will require a careful balance between data privacy and public health, and rigorous human-AI interaction. It is unlikely that these will be addressed in time to be of much help during the present pandemic. In the meantime, extensive gathering of diagnostic data on who is infectious will be essential to save lives, train AI, and limit economic damages.