This book addresses wave-based imaging: that is, imaging of unknown media from recorded wave signals that have propagated through them. The typical problems that we consider are velocity estimation and reflector imaging. In the first case, we recover approximately, that is, we image the background propagation velocity of the medium from estimated travel times between sensors. In the second case, we detect and localize, that is, we image anomalies present in the medium from recorded sensor data. Although established methods to address these imaging problems are presented, the focus is on correlation-based or interferometric imaging techniques using illumination signals generated by uncontrolled ambient noise sources. These techniques have attracted a lot of attention recently because they open new possibilities for imaging, in seismology, in synthetic aperture radar and elsewhere, where illuminating sources are rare and often uncontrolled and the recording sensors are passive. Their analysis involves mathematical methods and results that we introduce here in a systematic way. In the first part of the book (Chapters 2–6) we address correlation-based imaging for homogeneous and smoothly varying media. In the second part of the book (Chapters 7–8) we consider scattering media. In the last chapters (Chapters 9–11) we use the mathematical tools presented and developed in this book to revisit and analyze recent imaging modalities that use correlation-based techniques.