Network on Chip (NoC) architectures provide scalable platforms for designing Systems on Chip (SoC) with large number of cores. Developing products and applications using an NoC architecture offers many challenges and opportunities. A tool which can map an application or a set of applications to a given NoC architecture will be essential. In this thesis we first survey current techniques and we present our proposals for mapping and scheduling of concurrent applications to NoCs with multithreaded processors as computational resources. NoC platforms are basically a special class of Multiprocessor Embedded Systems (MPES). Conventional MPES architectures are mostly bus-based and, thus, are exposed to potential difficulties regarding scalability and reusability. There has been a lot of research on MPES development including work on mapping and scheduling of applications. Many of these results can also be applied to NoC platforms. Mapping and scheduling are known to be computationally hard problems. A large range of exact and approximate optimization algorithms have been proposed for solving these problems. The methods include Branch-and–Bound (BB), constructive and transformative heuristics such as List Scheduling (LS), Genetic Algorithms (GA) and various types of Mathematical Programming algorithms. Concurrent applications are able to capture a typical embedded system which is multifunctional. Concurrent applications can be executed on an NoC which provides a large computational power with multiple on-chip computational resources. Improving the time performances of concurrent applications which are running on Network on Chip (NoC) architectures is mainly correlated with the ability of mapping and scheduling methodologies to exploit the Thread Level Parallelism (TLP) of concurrent applications through the available NoC parallelism. Matching the architectural parallelism to the application concurrency for obtaining good performance-cost tradeoffs is  another aspect of the problem. Multithreading is a technique for hiding long latencies of memory accesses, through the overlapped execution of several threads. Recently, Multi-Threaded Processors (MTPs) have been designed providing the architectural infrastructure to concurrently execute multiple threads at hardware level which, usually, results in a very low context switching overhead. Simultaneous Multi-Threaded Processors (SMTPs) are superscalar processor architectures which adaptively exploit the coarse grain and the fine grain parallelism of applications, by simultaneously executing instructions from several thread contexts. In this thesis we make a case for using SMTPs and MTPs as NoC resources and show that such a multiprocessor architecture provides better time performances than an NoC with solely General-purpose Processors (GP). We have developed a methodology for task mapping and scheduling to an NoC with mixed SMTP, MTP and GP resources, which aims to maximize the time performance of concurrent applications and to satisfy their soft deadlines. The developed methodology was evaluated on many configurations of NoC-based platforms with SMTP, MTP and GP resources. The experimental results demonstrate that the use of SMTPs and MTPs in NoC platforms can significantly speed-up applications.