Haptic rendering has been developing for decades with different rendering approaches and many factors that affect the stability when rendering rigid-body interactions have been investigated. To get an overall understanding of the challenges in haptic rendering, we approach this topic by conducting a systematic review. This review examines different haptic rendering approaches and how to deal with instability factors in rendering. A total of 25 papers are reviewed to answer the following questions: (1) what are the most common haptic rendering approaches for rigid-body interaction? and (2) what are the most important factors for instability of haptic rendering and how to address them? Through the process of investigating these questions, we get the insight that transparency can be further explored and technical terms to describe haptic rendering can be more standardized to push the topic forward.