Irregular applications comprise an increasingly important workload domain for many fields, including bioinformatics, chemistry, physics, social sciences and machine learning. Therefore, achieving high performance and energy efficiency in the execution of emerging irregular applications is of vital importance. This dissertation studies the root causes of inefficiency of irregular applications in modern computing systems, and fundamentally addresses such inefficiencies, by proposing low-overhead synchronization techniques among parallel threads in cooperation with well-crafted data access policies. We make four major contributions to accelerating irregular applications in different contexts including CPU and Near-Data-Processing (NDP) (or Processing-In-Memory (PIM)) systems. First, we design ColorTM, a novel parallel graph coloring algorithm for CPU systems that trades off using synchronization with lower data access costs. Second, we propose SmartPQ, an adaptive priority queue that achieves high performance under all various contention scenarios in Non-Uniform Memory Access CPU systems. Third, we introduce SynCron, the first practical hardware synchronization mechanism tailored for NDP systems. Fourth, we design SparseP, the first library for high-performance Sparse Matrix Vector Multiplication on real PIM systems. We demonstrate that the execution of irregular applications in CPU and NDP/PIM architectures can be significantly accelerated by co-designing lightweight synchronization approaches along with well-crafted data access policies. This dissertation bridges the gap between processor-centric CPU systems and memory-centric PIM systems in the critically-important area of irregular applications. We hope that this dissertation inspires future work in co-designing software algorithms with cutting-edge computing platforms to significantly accelerate emerging irregular applications.