Interconnection networks provide an effective means by which components of a system such as processors and memory modules communicate to provide reliable connectivity. This facilitates the realization of a highly efficient network design suitable for computational-intensive applications. Particularly, the use of multistage interconnection networks has unique advantages as the addition of extra stages helps to improve the network performance. However, this comes with challenges and trade-offs, which motivates researchers to explore various design options and architectural models to improve on its performance. A particular class of these networks is shuffle exchange network (SEN) which involves a symmetric N-input and N-output architecture built in stages of N/2 switching elements each. This paper presents recent advances in multistage interconnection networks with emphasis on SENs while discussing pertinent issues related to its design aspects, and taking lessons from the past and current literature. To achieve this objective, applications, motivating factors, architectures, shuffle exchange networks, and some of the performance evaluation techniques as well as their merits and demerits are discussed. Then, to capture the latest research trends in this area not covered in contemporary literature, this paper reviews very recent advancements in shuffle exchange multistage interconnection networks within the last few years and provides design guidelines as well as recommendations for future consideration.