Voice is a natural mode of expression offered by modern computer-based systems. Qualitative perspectives on voice-based user experiences (voice UX) offer rich descriptions of complex interactions that numbers alone cannot fully represent. We conducted a systematic review of the literature on qualitative approaches to voice UX, capturing the nature of this body of work in a systematic map and offering a qualitative synthesis of findings. We highlight the benefits of qualitative methods for voice UX research, identify opportunities for increasing rigour in methods and outcomes, and distill patterns of experience across a diversity of devices and modes of qualitative praxis.