Biomechanical properties of soft tissues are important indicators of tissue functions which can be used for clinical diagnosis and disease monitoring. Elastography, incorporating the principles of elasticity measurements into imaging modalities, provides quantitative assessment of elastic properties of biological tissues. Benefiting from high-resolution, noninvasive and three-dimensional optical coherence tomography (OCT), optical coherence elastography (OCE) is an emerging optical imaging modality to characterize and map biomechanical properties of soft tissues. Recently, acoustic radiation force (ARF) OCE has been developed for elasticity measurements of ocular tissues, detection of vascular lesions and monitoring of blood coagulation based on remote and noninvasive ARF excitation to both internal and superficial tissues. Here, we describe the advantages of the ARF-OCE technique, the measurement methods in ARF-OCE, the applications in biomedical detection, current challenges and advances. ARF-OCE technology has the potential to become a powerful tool for in vivo elasticity assessment of biological samples in a non-contact, non-invasive and high-resolution nature.