Mobile cloud computing (MCC) enables the development of computational intensive mobile applications by leveraging the application processing services of computational clouds. Contemporary distributed application processing frameworks use runtime partitioning of elastic applications in which additional computing resources are occurred in runtime application profiling and partitioning. A number of recent studies have highlighted the different aspects of MCC. Current studies, however, have overlooked into the mechanism of application partitioning for MCC. We consider application partitioning to be an independent aspect of dynamic computational offloading and therefore we review the current status of application partitioning algorithms (APAs) to identify the issues and challenges. To the best of our knowledge, this paper is the first to propose a thematic taxonomy for APAs in MCC. The APAs are reviewed comprehensively to qualitatively analyze the implications and critical aspects. Furthermore, the APAs are analyzed based on partitioning granularity, partitioning objective, partitioning model, programming language support, presence of a profiler, allocation decision, analysis technique, and annotation. This paper also highlights the issues and challenges in partitioning of elastic application to assist in selecting appropriate research domains and exploring lightweight techniques of distributed application processing in MCC.