The evolution of wireless communication networks from 5G to emerging 6G technologies has fundamentally transformed network monitoring and management requirements, necessitating sophisticated real-time monitoring systems capable of operating at microsecond timescales while maintaining comprehensive visibility across distributed network elements. This technical review examines three critical domains in real-time monitoring systems: low-latency distributed tracing with eBPF integration that enables direct kernel-level instrumentation with minimal performance impact, digital twin networks for predictive optimization that create virtual replicas of physical network infrastructure for proactive management, and quantum-secure monitoring frameworks designed to operate effectively in post-quantum cryptographic environments. The convergence of edge computing, cloud-native architectures, and ultra-low latency applications has created unprecedented demands for monitoring solutions that can process massive telemetry data volumes while maintaining microsecond-level precision in event correlation and autonomous network optimization capabilities. These advanced monitoring systems extend beyond traditional network performance metrics to encompass security, quality of service, and autonomous optimization capabilities essential for supporting Industry 4.0, Internet of Things, and mission-critical applications that rely on telecommunications networks as foundational infrastructure.