The overall goal of this thesis is to develop non-linear Bayesian methods for three-dimensional tracking of a moving acoustic source in shallow water despite environmental uncertainty, with application to data from a horizontal line array (HLA) of hydrophones. As a precursor, Bayesian geoacoustic inversion is applied to estimate seabed model parameters and their uncertainties. A simulation study examines the effect of source and array factors on geoacoustic information content in matched-field inversion of HLA data, as quantified in terms of model parameter uncertainties. Bayesian geoacoustic inversion is applied to both controlled-source and ship-noise data from a HLA deployed on the seafloor in a shallow-water experiment conducted in the Barents Sea. A new approach is introduced to account for data error reduction due to averaging data over time-series subsegments (snapshots), based on empirically apportioning measurement and theory error, with effects on inversion results compared to those of existing approaches. It is further demonstrated that combining data from multiple, independent time-series segments (for a moving source) in the inversion can significantly reduce geoacoustic parameter uncertainties. Geoacoustic uncertainties are also shown to depend on ship range and orientation, with lowest uncertainties for short ranges and for the ship stern/propeller oriented toward the array. Sediment sound-speed profile and density estimates from controlled-source and ship-noise data inversions are found to be in good agreement with values from geophysical measurements. Two non-linear Bayesian matched-field inversion approaches are developed for three-dimensional source tracking despite environmental uncertainty. Focalization-tracking maximizes the posterior probability density (PPD) over track and environmental parameters. Synthetic test cases show that the algorithm substantially outperforms tracking with poor environmental estimates and generally obtains results close to those achieved with exact environmental knowledge. Marginalization-tracking integrates the PPD over environmental parameters to obtain joint marginal distributions over source coordinates, from which track uncertainty estimates and the most probable track are extracted. Both approaches are applied to data from the Barents Sea experiment. Focalization-tracking successfully estimates the tracks of the towed source and a surface ship in cases where simpler tracking algorithms fail. Marginalization-tracking generally outperforms focalization-tracking and gives uncertainty estimates that encompass the true tracks.