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The unabated flurry of research activities to augment various mobile devices by leveraging heterogeneous cloud resources has created a new research domain called Mobile Cloud Computing (MCC). In the core of such a non-uniform environment, facilitating interoperability, portability, and integration among heterogeneous platforms is nontrivial. Building such facilitators in MCC requires investigations to understand heterogeneity and its challenges over the roots. Although there are many research studies in mobile computing and cloud computing, convergence of these two areas grants further academic efforts towards flourishing MCC. In this paper, we define MCC, explain its major challenges, discuss heterogeneity in convergent computing (i.e. mobile computing and cloud computing) and networking (wired and wireless networks), and divide it into two dimensions, namely vertical and horizontal. Heterogeneity roots are analyzed and taxonomized as hardware, platform, feature, API, and network. Multidimensional heterogeneity in MCC results in application and code fragmentation problems that impede development of cross-platform mobile applications which is mathematically described. The impacts of heterogeneity in MCC are investigated, related opportunities and challenges are identified, and predominant heterogeneity handling approaches like virtualization, middleware, and service oriented architecture (SOA) are discussed. We outline open issues that help in identifying new research directions in MCC.