Passive acoustic monitoring (PAM) is a nonintrusive approach to studying behaviors of vocalizing marine organisms underwater that otherwise would remain unexplored. In this paper, we propose a data processing chain that can detect and track multiple whales in 3-D from passively recorded underwater acoustic signals. In particular, time-difference-of-arrival (TDOA) measurements of echolocation clicks are extracted from a volumetric hydrophone array's acoustic data by using a noise-whitening cross-correlation. For multi-target tracking, the TDOA measurements are then processed by a Bayesian inference engine consisting of two stages that is based on the sum-product algorithm (SPA). Particle flow is embedded in the SPA to make tracking computationally feasible in the considered nonlinear and high-dimensional scenario. The capability to track multiple whales without human intervention is demonstrated in scenarios with simulated and real data.