The focus of the building industry and research is shifting from delivering satisfactory spaces to going beyond what is merely acceptable with a wave of new research and practice dedicated to exploring how the built environment can support task performance and enhance people’s health and well-being. The present study addresses the role of acoustics in this paradigm shift. Indoor soundscape research has recently emerged as an approach that brings a perceptual perspective on building and room acoustics in order to shape built environments that “sound good” according to building occupants’ preference and needs. This paper establishes an initial discussion over some of the open questions in this field of research that is still in an embryonic stage. A thematic analysis of structured interviews with a panel of experts offered a range of perspectives on the characterization, management, and design of indoor soundscapes and health-related outcomes. The discussion pointed out the importance of both perceptual and multisensory research and integrated participatory design practices to enable a holistic view regarding the complex building–user interrelations and the design of just cities. Soundscape methodologies tailored to the peculiarities of indoor soundscapes can help to measure and predict the human perceptual response to the acoustic stimuli in context, thus reducing the risk of mismatches between expected and real building experiences. This perceptual perspective is expected to widen the scientific evidence for the negative and positive impacts of the acoustic environment on human health, well-being, and quality of life. This will support prioritizing the role of acoustics in building design and challenge many current design practices that are based on a noise control approach.