Vehicle re-identification (v-reID) is a crucial and challenging task in the intelligent transportation systems (ITS). While vehicle re-identification plays a role in analysing traffic behaviour, criminal investigation, or automatic toll collection, it is also a key component for the construction of smart cities. With the recent introduction of transformer models and their rapid development in computer vision, vehicle re-identification has also made significant progress in performance and development over 2021-2023. This bite-sized review is the first to summarize existing works in vehicle re-identification using pure transformer models and examine their capabilities. We introduce the various applications and challenges, different datasets, evaluation strategies and loss functions in v-reID. A comparison between existing state-of-the-art methods based on different research areas is then provided. Finally, we discuss possible future research directions and provide a checklist on how to implement a v-reID model. This checklist is useful for an interested researcher or practitioner who is starting their work in this field, and also for anyone who seeks an insight into how to implement an AI model in computer vision using v-reID.