The lateral line organ of fish has inspired engineers to develop flow sensor arrays— dubbed artificial lateral lines (ALLs)—capable of detecting near-field hydrodynamic events for obstacle avoidance and object detection. In this paper, we present a comprehensive review and comparison of ten localisation algorithms for ALLs. Differences in the studied domain, sensor sensitivity axes, and available data prevent a fair comparison between these algorithms from their original works. We compare them with our novel quadrature method (QM), which is based on a geometric property specific to 2D-sensitive ALLs. We show how the area in which each algorithm can accurately determine the position and orientation of a simulated dipole source is affected by (1) the amount of training and optimisation data, and (2) the sensitivity axes of the sensors. Overall, we find that each algorithm benefits from 2D-sensitive sensors, with alternating sensitivity axes as the second-best configuration. From the machine learning approaches, an MLP required an impractically large training set to approach the optimisation-based algorithms’ performance. Regardless of the data set size, QM performs best with both a large area for accurate predictions and a small tail of large errors.