: In this presentation, a short outline of the history of past and present Grid projects in research and industry is given, followed by some near- and long-term Grid scenarios and visions on how data and compute Grids will complement current Internet services and thus change our working and living environments and habits. In essence, implementation and professional exploitation of the complex and highly sophisticated Grid technologies will still take a couple of years and give us time enough to adapt to the dramatic changes and potential opportunities Grids will create in the future.