Observability in Large Language Models (LLMs) is crucial for understanding, evaluating, and optimizing their non-deterministic and resource-intensive performance in AI applications like chatbots and retrieval-augmented generation systems. Unlike traditional monitoring, observability in LLMs focuses on understanding the "why" behind system behaviors, incorporating the MELT framework—Metrics, Events, Logs, and Traces—to offer insights into system performance and behavior. This framework is expanded with LLM-specific components such as prompts, user feedback, and evaluations to refine model outputs and align them with user expectations. Implementing observability in production involves challenges such as tracing complex workflows, managing high resource demands, and maintaining output consistency, which necessitate tools like Splunk, Prometheus, and Grafana for data collection, resource monitoring, and visualization. Additionally, leveraging modern tools like LangSmith, Langfuse, and SigNoz enhances observability practices by providing capabilities tailored to LLM needs, including tracing, cost tracking, and quality evaluations. As LLM technologies evolve, future trends in observability will likely involve multi-modal model monitoring, edge deployments, AI-augmented anomaly detection, and ethical safeguards to ensure reliability, efficiency, and compliance in increasingly complex systems.