Although maritime transport is the backbone of world commerce, it is traditionally slow to adopt emerging technologies such as Digitalization and Artificial Intelligence (AI). In this presentation we summarize the current state of AI applications in the maritime sector, making a clear distinction between important – but still promising – research efforts, and mature AI solutions which are readily available for use by the maritime companies. The state-of-the-art of AI in the maritime sector can be currently categorized in five broad domains: autonomous vessels and remote command systems; prediction-based route optimization and fuel efficiency, situational awareness and safety, optimization of port operations, AI solutions in the back-office. The most interesting examples of vendors offering AI solutions in the maritime industry are briefly reviewed, illustrating the ever-increasing interest on the subject, arising from the necessity of raising the rate of AI adoption in the maritime industry to the same level as other leading industries.