The importance of data is increasing along its inflation in our world today. In the big data era, data is becoming a main source for innovation, knowledge and insight, as well as a competitive and financial advantage in the race of information procurement. This interest in acquiring and exploiting data, in addition to the existing concerns regarding the privacy and security of information, raises the question of who should own the data and how the ownership of data can be preserved. This paper discusses and analyses the concept of data ownership and provides an overview on the subject from different point of views. It surveys also the state-of-the-art of data ownership in health, transportation, industry, energy and smart cities sectors and outlines lessons learned with an extended definition of data ownership that may pave the way for future research and work in this area.