Simple Summary: Aedes albopictus is a well-established competent arbovirus vector in Reunion Island, a French overseas territory in the Indian Ocean, occurring in a range of natural to urban environments where it represents a major threat to public health. Following the 2006 Chikungunya outbreak and periodic occurrence of dengue epidemics, the sterile insect technique (SIT) emerged as the most environment-friendly option for integration with the current vector control strategy that relies mainly on the elimination of breeding sites and insecticide applications. This paper describes the trajectory that has been followed in assessing the feasibility of SIT against Ae. albopictus in Reunion Island, and reviews some of the main achievements since 2009. These include essential scientific information so far obtained on the biology and ecology of Ae. albopictus, and the development of the requisite technological capabilities for the production and release of sexually competitive sterile males. Furthermore, it also draws attention to the strategies established to streamline the decision-making process, including an awareness campaign to enhance public understanding, efforts to secure public acceptance and regulatory validation of SIT pilot testing for small-scale suppression of wild Ae. albopictus in selected urban sites on the island. Abstract: The global expansion of Aedes albopictus, together with the absence of specific treatment and vaccines for most of the arboviruses it transmits, has stimulated the development of more sustainable and ecologically acceptable methods for control of disease transmission through the suppression of natural vector populations. The sterile insect technique (SIT) is rapidly evolving as an additional tool for mosquito control, offering an efficient and more environment-friendly alternative to the use of insecticides. Following the devastating chikungunya outbreak, which affected 38% of the population on Reunion Island (a French overseas territory in the southwest of the Indian Ocean), there has been strong interest and political will to develop effective alternatives to the existing vector control strategies. Over the past 10 years, the French Research and Development Institute (IRD) has established an SIT feasibility program against Ae. albopictus on Reunion Island in collaboration with national and international partners. This program aimed to Insects 2020, 11, 770 2 of 25 determine whether the SIT based on the release of radiation-sterilized males is scientifically and technically feasible, and socially acceptable as part of a control strategy targeting the local Ae. albopictus population. This paper provides a review of a multi-year and a particularly broad scoping process of establishing the scientific and technological feasibility of the SIT against Ae. albopictus on Reunion Island. It also draws attention to some prerequisites of the decision-making process, through awareness campaigns to enhance public understanding and support, social adoption, and regulatory validation of the SIT pilot tests.