With the development of the entertainment industry, the need for immersive and emotionally impactful sound design has emerged. Utilization of spatial sound is potentially the next step to improve the audio experiences for listeners in terms of their emotional engagement. Hence, the relationship between spatial audio characteristics and emotional responses of the listeners has been the main focus of several recent studies. This paper provides a systematic overview of the above reports, including the analysis of commonly utilized methodology and technology. The survey was undertaken using four literature repositories, namely, Google Scholar, Scopus, IEEE Xplore, and AES E-Library. The overviewed papers were selected according to the empirical validity and quality of the reported studies. According to the survey outcomes, there is growing evidence of a positive influence of the selected spatial audio characteristics on the listeners’ affective responses. However, more data is required to build reliable, universal, and useful models explaining the above relationship. Furthermore, the two research trends on this topic were identified. Namely, the studies undertaken so far can be classified as either technology-oriented or technology-agnostic, depending on the research questions or experimental factors examined. Prospective future research directions regarding this topic are identified and discussed. They include better utilization of scene-based paradigms, affective computing techniques, and exploring the emotional effects of dynamic changes in spatial audio scenes.