Cloud computing has emerged rapidly as a growing paradigm of on-demand access to computing, data and software utilities using a usage-based billing model. Users essentially rent resources and pay for what they use and everything including software, platform, and infrastructure is as a service. In this talk, I will give a review of supercomputing, cluster computing, grid computing and cloud computing. Comparisons of these computing domains and programming models, their limitations and potential solutions will be included in this talk. In particular, I will point out the shortcomings and limitations of current cloud computing programming models and propose possible solutions. Current MapReduce model and its variants have succeeded in data-parallel applications such as database operations and web searching; however, they are still not effective for compute-intensive applications such as many graph applications. We propose several approaches to solving this problem through extension of current programming models, automatic translation from sequential codes to cloud codes, detection of data and task parallelism and effective scheduling on cloud programming models. Some preliminary theoretical and experimental results will also be reported in this talk.