Sound source localization with sensor arrays involves the estimation of the direction-of-arrival (DOA) from a limited number of observations. Compressive sensing (CS) solves such underdetermined problems achieving sparsity, thus improved resolution, and can be solved efficiently with convex optimization. The DOA estimation problem is formulated in the CS framework and it is shown that CS has superior performance compared to traditional DOA estimation methods especially under challenging scenarios such as coherent arrivals and single-snapshot data. An offset and resolution analysis is performed to indicate the limitations of CS. It is shown that the limitations are related to the beampattern, thus can be predicted. The high-resolution capabilities and the robustness of CS are demonstrated on experimental array data from ocean acoustic measurements for source tracking with single-snapshot data.