The usability of Mobile devices and portable computers has been increased very rapidly. The main focus of modern research is to handle the big data in Mobile and pervasive computing. This paper gives an overview of Mobile Data Challenge which was a smart phone based research done by Nokia through Lausanne Data Collection Campaign. The Mobile Data Challenge was introduced when the amount of mobile data was seen to be increased very much in a short period of time. The rise of big data demands that this data can be accessed from everywhere and anytime. For handling such a huge amount of data e.g. SMS, images, videos etc, this data must be compressed for easy transmission over the network. It also helps in reducing the storage requirements. There are various techniques for the compression of data that are discussed in this paper. SMAZ and ShortBWT techniques are used to compress SMS. JPEG and Anamorphic Stretch Transform are used to compress the images. 

Big data management (BDM) is the administration, management and governance of large volumes of all types of structured, semi-structured and unstructured data. Big data management is a blend of old and new best practices, teams, data types, skills, and home-grown or industrial-built functions and methods. Big Data Management is at the genesis of massive change to technology that will spur massive societal and industrial change. In this paper, different key factors kept in mind while managing big data are discussed along with the process of managing data so that organisations can get secure and accurate data. Further different developers have introduced methods have also been discussed and with it the main tools used in management of Big Data are introduced in this paper. BDM is suffering from many issues in the world are also explained here. Big Data Management deals with the integration, manipulation, quality and governance and management of Big Data including the key factors- Volume, Velocity and Variety of Big Data.