The continuous increasing in performance requirements, for both scientic computation and industry, motivates the need of a powerful computing infrastructure. The Grid appeared as a solution for inexpensive execution of heavy applications in a parallel and distributed manner. It allows joining resources independently of their physical location and architecture to form a global resource pool available to all grid users. However, grid environments are highly unstable and unpredictable. Adaptability is a crucial issue in this context, in order to guarantee an appropriate quality of service to users. Migration is a technique frequently used for achieving adaptation. The objective of this report is to survey the problem of strong migration in heterogeneous environments like the grids', the related issues and the current solutions. 1