The excessive amounts of data generated by devices and Internet-based sources at a regular basis constitute, big data. This data can be processed and analyzed to develop useful applications for specific domains. Several mathematical and data analytics techniques have found use in this sphere. This has given rise to the development of computing models and tools for big data computing. However, the storage and processing requirements are overwhelming for traditional systems and technologies. Therefore, there is a need for infrastructures that can adjust the storage and processing capability in accordance with the changing data dimensions.Cloud Computing serves as a potential solution to this problem. However, big data computing in the cloud has its own set of challenges and research issues. This chapter surveys the big data concept, discusses the mathematical and data analytics techniques that can be used for big data and gives taxonomy of the existing tools, frameworks and platforms available for different big data computing models. Besides this, it also evaluates the viability of cloud-based big data computing, examines existing challenges and opportunities, and provides future research directions in this field.