Audio Augmented Reality (AAR) aims to augment people's auditory perception of the real world by synthesizing virtual spatialized sounds. AAR has begun to attract more research interest in recent years, especially because Augmented Reality (AR) applications are becoming more commonly available on mobile and wearable devices. However, because audio augmentation is relatively under-studied in the wider AR community, AAR needs to be further investigated in order to be widely used in different applications. This paper systematically reports on the technologies used in past studies to realize AAR and provides an overview of AAR applications. A total of 563 publications indexed on Scopus and Google Scholar were reviewed, and from these, 117 of the most impactful papers were identified and summarized in more detail. As one of the first systematic reviews of AAR, this paper presents an overall landscape of AAR, discusses the development trends in techniques and applications, and indicates challenges and opportunities for future research. For researchers and practitioners in related fields, this review aims to provide inspirations and guidance for conducting AAR research in the future.