Wide bandgap (WBG) devices are becoming increasingly popular due to their excellent material properties. WBG devices are commercially available in discrete and module packages. Many studies have investigated the design, structure and benefits of module packages. However, a comprehensive and in-depth overview of the discrete package is lacking. Discrete package has the advantages of flexibility, scalability and reduced cost; however, challenges of severe switching oscillations and limited current capacity are associated with it. This review encompasses the switching oscillations and limited current capacity issues of discrete devices. Switching oscillations are categorized in terms of voltage. The underlying oscillation mechanisms are explored in detail. For the current imbalance, the types, root causes and adverse effects in parallel-connected discrete devices application are reviewed. Besides, the most recent techniques to extract stray parameters are also explored. Finally, state-of-the-art methods to mitigate the switching oscillations and the current imbalance are summarized and evaluated. The performance improvement strategies discussed in this paper can assist researchers to better use the discrete package and can stimulate them to come up with new solutions.