In modern data-centric wireless networks, caching alleviates severe capacity crunch at times of high network load. Recent results have shown that careful design of cache storage to leverage coded multicast file delivery over a shared link can achieve order-wise improvements in the storage-rate trade-off. In this work, we present a novel caching and delivery scheme for the case when users have heterogeneous cache sizes. The proposed scheme uses two new ingredients namely set partitioning and cache layering. The main challenge in designing caching schemes in presence of storage heterogeneity is that varying levels of storage across users can present a variety of caching and multicasting opportunities. Our framework of cache layering and set partitioning is a principled approach to utilize such opportunities, where each layer delivers a fraction of requested data to a specific set of users and layers operate independently of each other. We also derive an information-theoretic lower bound for the heterogeneous caching problem.