Computation task offloading is one of the enabling technologies for computation-intensive applications and edge intelligence, which experiences the explosive growth of massive data generated. Different techniques, wireless technologies and mechanisms have been proposed in the literature for task offloading in order to improve the services provided to the users. Although there is a rich literature of computation task offloading, the role of data in the scope of it has not received much attention yet. This motivates us to propose a survey which classified the state-of-the-art (SoTA) of computation task offloading from the view point of data. First, a thorough literature review is conducted to reveal the SoTA from various aspects with the consideration of task generation, i.e., architecture, objective, offloading strategy, task types, etc. It is found that types of task offloading is related to the data and will affect the offloading procedure, which contains resource allocation, task allocation etc. Then computation offloading is classified into two categories based on task types, namely static task based offloading and dynamic task based offloading. Finally, our views on future computation offloading are provided with the corresponding challenges and opportunities.