The accurate prediction of atmospheric low-visibility events due to fog, haze or atmospheric pollution is an extremely important problem, with major consequences for transportation systems, and with alternative applications in agriculture, forest ecology and ecosystems management. In this paper, we provide a comprehensive literature review and analysis of AI-based methods applied to fog and low-visibility events forecasting. We also discuss the main general issues which arise when dealing with AI-based techniques in this kind of problem, open research questions, novel AI approaches and data sources which can be exploited. Finally, the most important new AI-based methodologies which can improve atmospheric visibility forecasting are also revised, including computational experiments on the application of ordinal classification approaches to a problem of low-visibility events prediction in two Spanish airports from METAR data.