The advent of large language models (LLMs) creates new opportunities to conduct qualitative interviews at scale, with thousands of respondents, thereby bridging qualitative and quantitative methods. We develop a simple, versatile approach for researchers to run AI-led qualitative interviews, including voice interviews. We assess its robustness by drawing comparisons to human experts and with several respondents-based quality metrics. The versatility of the approach is illustrated through four broad classes of applications: eliciting key factors in decision making, political views, subjective mental states, and mental models of the effects of public policies. High performance ratings are obtained in all of these domains. Our applications highlight the potential of AI-led interviews as a tool for measurement, hypothesis generation, and discovering mechanisms.