Dengue infection is a mosquito-borne disease caused by dengue viruses, which are carried by several species of mosquito of the genus Aedes, principally Ae. aegypti. Dengue outbreaks are endemic in tropical and sub-tropical regions of the world, mainly in urban and sub-urban areas. The outbreak is one of the top ten diseases causing the most deaths worldwide. According to the World Health Organization (WHO), dengue infection has increased 30-fold globally over the past five decades. About 50 to 100 million new infections occur annually in more than 80 countries. Many researchers are working on measures to prevent and control the spread. One avenue of research is collaboration between computer science and the epidemiology researchers in developing methods of predicting potential outbreaks of dengue infection. An important research objective is to develop models that enable, or enhance, forecasting of outbreaks of dengue, giving medical professionals the opportunity to develop plans for handling the outbreak, well in advance. Researchers have been gathering and analyzing data to better identify the relational factors driving the spread of the disease, as well as the development of a variety of methods of predictive modelling using statistical and mathematical analysis and Machine Learning. In this substantial review of the literature on the state of the art of research over the past decades, we identified six main issues to be explored and analyzed: (1) The available data sources, (2) Data preparation techniques, (3) Data representations, (4) Forecasting models and methods, (5) Dengue forecasting models evaluation approaches, and (6) Future challenges and possibilities in forecasting modelling of dengue outbreaks. Our comprehensive exploration of the issues provides a valuable information foundation for new researchers in this important area of public health research and epidemiology.