The advancement of mobile cloud computing (MCC) has the potential to improve communication and information during disaster emergency operation. Many studies from different countries have addressed different approaches to implement mobile cloud technologies during disaster operation. However, there has been a lack of any consolidated evidencebased study to evaluate the MCC from the dual perspectives of disaster emergency situation and technology. In this paper, we provide an extensive study of mobile cloud computing research as a critical system or application based on the latest literature published from 2010 to 2015, and highlights the specific challenges in implementing mobile cloud computing in disaster emergency operation. A systematic literature review was conducted over 4 prominent journals of computer science engineering (IEEE, ACM, ProQuest, Inspec / Elsevier) and the findings were classified into four key challenges of MCC implementation during disaster emergency operation. We present a taxonomy based on the key challenges in this area, and discuss the different solutions taken to solve the challenges. We conclude the paper with a critical analysis of the challenges that have not been solved, and highlight directions for future work.