Now a day the architecture of high performance systems are improving with more and more processor cores on the chip. This has both benefits as well as challenges. The benefit is running more task simultaneously which reduces the running time of the program or application. The challenges are what is the maximum limit of the number of cores in the given chip, how the existing and future software will make use of all the cores, what parallel programming language to choose, what are the memory and cache coherence issues involved when we increase the number of cores, how to solve the power and performance issues, how the cores are connected and how they are communicating to solve a single problem, workload distribution and load balancing issues in terms of scalability. There is a practical limit for speedup and scalability of number of cores on the chip which needs to be analyzed. So this chapter will focus on the introduction and overviews of parallel computing and the challenges faced in enhancing the performance and scalability in parallel computing architecture.