This paper is concerned with the localization of clicking Blainville's beaked whales (Mesoplodon densirostris) using an array of widely spaced bottom-mounted hydrophones. A set of signal and data processing advances are presented that together make reliable tracking a possibility. These advances include a species-specific detector, elimination of spurious time-difference-of-arrival (TDOA) estimates, improved tracking of TDOA estimates, positive association of TDOA estimates using different hydrophone pairs, and joint localization of multiple whales. A key innovation in three of these advances is the principle of click-matching. The methods are demonstrated using real data.