Just as beamforming matched filter sonar (BMF) provides a simple model for the sonar of bats and dolphins, so do recently developed matched-field processing sonars (MFP) provide simple models for the sonar of humpbacks and other mysticetes. This talk reviews the principles of MFP sonar and the behaviors essential to its use. As BMF is optimal for locating small, nearby, rapidly moving targets (potential prey), so is MFP sonar optimal for locating large, distant, slow-moving targets (potential mates). While BMF uses mainly the direct echo from a target, MFP sonar uses the complete reflected wavetrain, matching the latter with the convolution of the source and a set of empirical Green's functions. MFP sonar requires lower frequencies, more power, and longer listening times than BMF sonar, which is why humpback sound sequences consist of long patterns of regularly spaced sweeps rather than the click trains of odontocetes. Observations of dolphins show their expertise at BMF; similarly, the careful acoustic and visual observations of humpbacks by Payne, Tyack, Herman, Frankel and others show the expertise of humpbacks at MFP sonar. Their observations suggest that when a singer continues to sing after being joined by a nonsinger, the joiner is likely an immature male learning to echolocate; also, the rapid convergence of humpback whale song is a trait selected to impede the use of singer echoes by nonsinging males.