Pipelines are used in many sectors to transport materials such as fluid from one place to another. These pipelines require regular inspection and maintenance to ensure proper operations and to avoid accidents. Many in-pipe navigation robots have been developed to perform the inspection. Soft in-pipe navigation robot is a special class of in-pipe robot, where the structure is made entirely of soft materials. The soft in-pipe robots are cheaper, lightweight, robust, and more adaptable to the environment inside pipelines as compared to the traditional rigid in-pipe navigation robot. This paper reviews the design of different types of soft in-pipe navigation in terms of the material, structure, locomotion strategy, and actuation techniques. These four different aspects of the design help researchers to narrow down their research and explore different opportunities within each of the design aspects. This paper also offers suggestions on the direction of research to improve the current soft in-pipe navigation robot design.