Resource utilization has been studied as an optimization objective for generative large language models (LLMs). Recent studies show that this resource dependence can also be weaponized, as excessive generation, when scaled through high-volume requests, increases inference latency, undermines service availability, and threatens economic sustainability. However, these risks remain underexamined because existing studies are fragmented and their boundaries with legitimate, resource-intensive uses of LLMs are unclear. To address this gap, we provide a systematic review of threats to resource consumption in LLMs. Unlike surveys on inference acceleration, we focus on how resource consumption threats induce disruptive behaviors and synthesize existing studies into research strands that connect attack objectives, triggering mechanisms, and defenses. We further introduce an outcome-based severity taxonomy that distinguishes bounded, non-degenerate Overthinking from self-sustaining Unbounded Drift, providing operational criteria for characterizing adversarial resource consumption. Our goal is to clarify this emerging threat landscape and support future characterization, evaluation, and mitigation. The project repository is publicly available at https://anonymous.4open.science/r/RCT-LLM/.