The field of artificial intelligence has undergone a revolution from foundational Transformer architectures to reasoning-capable systems approaching human-level performance. We present LLMOrbit, a comprehensive circular taxonomy navigating the landscape of large language models spanning 2019-2025. This survey examines over 50 models across 15 organizations through eight interconnected orbital dimensions, documenting architectural innovations, training methodologies, and efficiency patterns defining modern LLMs, generative AI, and agentic systems. We identify three critical crises: (1) data scarcity (9-27T tokens depleted by 2026-2028), (2) exponential cost growth ($3M to $300M+ in 5 years), and (3) unsustainable energy consumption (22x increase), establishing the scaling wall limiting brute-force approaches. Our analysis reveals six paradigms breaking this wall: (1) test-time compute (o1, DeepSeek-R1 achieve GPT-4 performance with 10x inference compute), (2) quantization (4-8x compression), (3) distributed edge computing (10x cost reduction), (4) model merging, (5) efficient training (ORPO reduces memory 50%), and (6) small specialized models (Phi-4 14B matches larger models). Three paradigm shifts emerge: (1) post-training gains (RLHF, GRPO, pure RL contribute substantially, DeepSeek-R1 achieving 79.8% MATH), (2) efficiency revolution (MoE routing 18x efficiency, Multi-head Latent Attention 8x KV cache compression enables GPT-4-level performance at $<$$0.30/M tokens), and (3) democratization (open-source Llama 3 88.6% MMLU surpasses GPT-4 86.4%). We provide insights into techniques (RLHF, PPO, DPO, GRPO, ORPO), trace evolution from passive generation to tool-using agents (ReAct, RAG, multi-agent systems), and analyze post-training innovations.