Acoustic emission monitoring is widely used for damage detection in materials research and for site monitoring. Its use for masonry structures is however challenging due to the highly heterogenic nature of masonry and rapid signal attenuation. However, the non-invasive nature and high sensitivity of the technique also provide interesting opportunities, especially for historical masonry structures, to locate damage, identify severity of damage and rate of deterioration. Aim of this paper is to provide an extensive literature review on the application of the acoustic emission technique for masonry structures, addressing specific challenges and recent findings. AE-based methods for damage assessment in masonry are discussed in view of monitoring approaches, wave propagation, source location and crack development under static, fatigue and creep loading. Site applications are discussed for identifying crack location and crack propagation in historical masonry towers, buildings and masonry arch bridges. The paper concludes with future challenges identified in this research field.