Body undulation used by snakes and the physical architecture of a snake body may offer significant benefits over typical legged or wheeled locomotion designs in certain types of scenarios. A large number of research groups have developed snake-inspired robots to exploit these benefits. The purpose of this review is to report different types of snake-inspired robot designs and categorize them based on their main characteristics. For each category, we discuss their relative advantages and disadvantages. This review will assist in familiarizing a newcomer to the field with the existing designs and their distinguishing features. We hope that by studying existing robots, future designers will be able to create new designs by adopting features from successful robots. The review also summarizes the design challenges associated with the further advancement of the field and deploying snake-inspired robots in practice.