Meta's Large Language Models (LLMs)---the Llama model family---serve nearly one billion monthly active users. Deploying these models for inference involves navigating a complex design space that spans diverse hardware options (e.g., H100, H200, MI300X), multiple parallelism strategies (tensor, pipeline, expert, context, and data parallelism), and nuanced runtime choices (e.g., continuous batching versus prefill-decode disaggregation)---all while leveraging workload-specific characteristics and meeting stringent service level objectives (SLOs). This paper presents insights we gained from developing and applying a systematic approach to analyze millions of deployment configurations and identify those that maximize throughput while meeting latency SLOs. We share lessons learned from our experience operating Llama inference at scale, including trade-offs among runtime designs, the phase-specific nature of parallelism strategies, opportunities for leveraging hardware heterogeneity, platform scaling behaviors, and system-level implications of model architectures such as Mixture-of-Experts (MoE). We hope our production experience offers practical insights for the broader LLM inference community.