With the advance of computational technologies, the applications running on modern distributed systems became more and more complex. Large-scale applications like environmental applications require such an amount of computation powers on demand that a single computing system hardly can provide. One of the solutions is Grid technologies that connect distributed computational resources of dynamic multi-institutional virtual organizations together and provide aggregate computational powers for solving very complex and computation demanding problems. The technologies make the infrastructures for researchers to share resources and knowledge, allows them to collaborate on solving common problems. The other solution is Cloud computing technologies that deliver computational resources via the Internet in a pay-per-use and self-service way. The technologies allow business and enterprises to use external computational resources dynamically on demands what can reduce the cost of IT resources and allow company to adapt quickly to change of business environment. The research and developments in European projects reflect the eventual change of requirements from applications, advantages and obstacles of the mentioned technologies and mainly the transition from Grid to Cloud computing.