Distributed systems for real-time applications have become essential in modern computing environments where speed, scalability, and reliability are critical requirements. These systems enable multiple interconnected nodes to process and share data simultaneously, ensuring timely responses for applications such as financial trading, healthcare monitoring, industrial automation, and autonomous systems. This paper explores the fundamental concepts, architecture, and technologies that support distributed real-time computing, including synchronization mechanisms, load balancing, fault tolerance, and communication protocols. It highlights how distributed architectures improve system performance by enabling parallel processing and reducing latency. The study also examines key challenges such as network delays, consistency issues, system failures, and resource management complexities. Furthermore, it discusses advanced solutions such as edge computing, in-memory processing, and real-time stream processing frameworks. The findings emphasize that distributed systems play a crucial role in enabling high-performance real-time applications across various industries.