The proposed research work discusses issues concerning the "Algorithms and tools for mapping and executing applications onto distributed and heterogeneous systems" scientific area. The discussed research work is conducted at the Parallel and Distributed Systems Group in the Department of Informatics of the Aristotle University of Thessaloniki under the supervision of Professor Dr. Helen Karatza. In our previous efforts, we have extensively dealt with the discovery of resources and the efficient mapping of applications in large-scale heterogeneous distributed environments. In order to efficiently identify appropriate resources for certain applications, we enhanced the proposed mechanisms with a matchmaking framework. Moreover, our research took the direction of managing the uncertainties encountered in such environments by proposing a mechanism able to overcome the phenomenon of resource failures. As for future research directions, we intend to deal with efficient mapping mechanisms that take into consideration the "resource evolution" phenomenon, weighing in the technical changes that so commonly occur in the resources of distributed environments. Finally, we intend to deal extensively in the direction of trusted mapping and directing applications to reliable resources in a distributed environment. The objective of this research direction is to provide robustness to distributed environments against malicious behaviours.