A real-time system must execute functionally correct computations in a timely manner. Most of the current real-time systems are static in nature. However in recent years, the growing need for building complex real-time applications coupled with advancements in information technology drives the need for dynamic real-time systems. Dynamic real-time systems need to be designed not only to deal with expected load scenarios, but also to handle overloads by allowing graceful degradation in system performance. Value-based scheduling is a means by which graceful degradation can be achieved by executing critical tasks that offer high values/benefits/rewards to the functioning of the system. This thesis identifies the following two issues in dynamic real-time scheduling: (i) maintaining high system reliability without affecting its schedulability and (ii) providing graceful degradation to the system during overload and maintaining high schedulability during underloads or near full loads. Further, we use value-based scheduling techniques to address these issues. The first contribution of this thesis is a reliability-aware value-based scheduler capable of maintaining high system reliability and schedulability. We use a performance index (PI) based value function for scheduling, which can capture the tradeoff between schedulability and reliability. The proposed scheduler selects a suitable redundancy level for each task so as to increase the performance index of the system. We show through our simulation studies that proposed scheduler maintains a high system value (PI). The second contribution of this thesis is an adaptive value-based scheduler that can change its scheduling behavior from deadline-based scheduling to value-based scheduling based on the system workload, so that it can maintain a high system value with fewer deadline misses. Further, the scheduler is extended to heterogeneous computing (HC) systems, wherein the computing capabilities of processors/machines are different, and propose two adaptive schedulers (Basic and Integrated) for HC systems. The performance of the proposed scheduling algorithms is studied through extensive simulation studies for both homogeneous and heterogeneous computing systems. We have concluded that the proposed adaptive scheduling scheme maintains a high system value with fewer deadlines misses for all range workloads. Amongst the schedulers for HC systems, we conclude that the Basic scheduler, which has a lesser run-time complexity, performs better for most of the workloads. The last contribution of this thesis is the design and implementation of the proposed adaptive value-based scheduler for homogeneous computing systems in a real-time Linux operating system, RT-Linux. We compare the performance of the implementation with EDF and Highest Value-Density First (HVDF) schedulers for various ranges of workloads and show that the proposed scheduler performs better in maintaining a high system value with fewer deadline misses.