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By pre-fetching popular videos into the local caches of edge nodes, wireless edge caching provides an effective means of reducing repeated content deliveries. To meet the various viewing quality requirements of multimedia users, scalable video coding (SVC) is integrated with edge caching, where the constituent layers of scalable videos are flexibly cached and transmitted to users. In this article, we discuss the challenges arising from the different content popularity and various viewing requirements of scalable videos, and present the diverse types of cached contents as well as the corresponding transmission schemes. We provide an overview of the existing caching schemes, and summarize the criteria of making caching decisions. A case study is then presented, where the transmission delay is quantified and used as the performance metric. Simulation results confirm that giving cognizance to the realistic requirements of end users is capable of significantly reducing the content transmission delay, compared to the existing caching schemes operating without SVC. The results also verify that the transmission delay of the proposed random caching scheme is lower than that of the caching scheme which only provides local caching gain.