Ultrasound elastography (USE) provides complementary information of tissue stiffness and elasticity to conventional ultrasound imaging. It is noninvasive and free of radiation, and has become a valuable tool to improve diagnostic performance with conventional ultrasound imaging. However, the diagnostic accuracy will be reduced due to high operator-dependence and intra- and inter-observer variability in visual observations of radiologists. Artificial intelligence (AI) has great potential to perform automatic medical image analysis tasks to provide a more objective, accurate and intelligent diagnosis. More recently, the enhanced diagnostic performance of AI applied to USE have been demonstrated for various disease evaluations. This review provides an overview of the basic concepts of USE and AI techniques for clinical radiologists and then introduces the applications of AI in USE imaging that focus on the following anatomical sites: liver, breast, thyroid and other organs for lesion detection and segmentation, machine learning (ML) - assisted classification and prognosis prediction. In addition, the existing challenges and future trends of AI in USE are also discussed.