Soft robotics enables unprecedented capabilities for mobile robots that could not be previously achieved using rigid mechanisms. This article serves as a reference for researchers working in soft robotic locomotion, provides classifications and trends in this field, and looks ahead to make recommendations for future developments. Soft robotic locomotion tends to be heavily bioinspired. Consequently, we provide a taxonomy of soft robotic locomotion according to locomotion mode, including crawling, flying, swimming, legged locomotion, jumping, and alternative locomotion techniques. For each locomotion mode, we investigate fundamental aspects including actuation type, speed, locomotion gaits, control type, and power autonomy to present an accurate snapshot of soft robotic locomotion research. During the investigation, we focus primarily on the robotics literature from 2016 to 2021, while including some of the seminal work from previous years. In this article, we provide a comprehensive overview of recent soft robotic locomotion research including a broad overview of soft robotic research in several aspects, such as locomotion applications, flexible substrates, and compliant mechanisms, as part of the larger domain of soft robotic locomotion. We also discuss the research trend recent years in this area, possible future research focus, and application of soft locomotion research in human-robot interaction occasions.