The Sussex-Huawei Locomotion-Transportation (SHL) Recognition Challenges aim to advance and capture the state-of-the-art in locomotion and transportation mode recognition from smartphone motion (inertial) sensors. The goal of this series of machine learning and data science challenges was to recognize eight locomotion and transportation activities (Still, Walk, Run, Bus, Car, Train, Subway). The three challenges focused on time-independent (SHL 2018), position-independent (SHL 2019) and user-independent (SHL 2020) evaluations, respectively. Overall, we received 48 submissions (out of 93 teams who registered interest) involving 201 scientists over the three years. The survey captures the state-of-the-art through a meta-analysis of the contributions to the three challenges, including approaches, recognition performance, computational requirements, software tools and frameworks used. It was shown that state-of-the-art methods can distinguish with relative ease most modes of transportation, although the differentiating between subtly distinct activities, such as rail transport (Train and Subway) and road transport (Bus and Car) still remains challenging. We summarize insightful methods from participants that could be employed to address practical challenges of transportation mode recognition, for instance, to tackle over-fitting, to employ robust representations, to exploit data augmentation, and to exploit smart post-processing techniques to improve performance. Finally, we present baseline results to compare the three challenges with a unified recognition pipeline and decision window length.