Medical robotics is an interdisciplinary field that came into existence to improve medical procedures utilizing robotics technology. Medical robotics range from minimally invasive surgeries using robots to robots that support patients in rehabilitation to image-guided systems for different medical interventions. Different advantages of robots made them appealing to be used for medical interventions. Among these advantages are being precise, untiring, dexterous, and the ability to work in environments that are not safe to human clinicians. Steerable needles are a type of medical devices that can steer around obstacles to reach a target location and thus can improve the accuracy of medical procedures. This paper provides a comprehensive review of the state-of-the-art and research challenges in robotic needle steering. First off, the motivations, including clinical motivations behind needle steering, are demonstrated, and then the state of the art of the different needle steering techniques in the literature are analyzed. This includes their modeling, path planning, control, and clinical applications. Finally, a discussion of the advantages and limitations of the existing techniques that hindered the clinical acceptance of the steerable needles, along with suggestions to get these needles closer to their clinical applications, as well as concluding remarks, is provided.