With the increasingly giant scales of (causal) large language models (LLMs), the inference efficiency comes as one of the core concerns along the improved performance. In contrast to the memory footprint, the latency bottleneck seems to be of greater importance as there can be billions of requests to a LLM (e.g., GPT-4) per day. The bottleneck is mainly due to the autoregressive innateness of LLMs, where tokens can only be generated sequentially during decoding. To alleviate the bottleneck, the idea of speculative execution, which originates from the field of computer architecture, is introduced to LLM decoding in a \textit{draft-then-verify} style. Under this regime, a sequence of tokens will be drafted in a fast pace by utilizing some heuristics, and then the tokens shall be verified in parallel by the LLM. As the costly sequential inference is parallelized, LLM decoding speed can be significantly boosted. Driven by the success of LLMs in recent couple of years, a growing literature in this direction has emerged. Yet, there lacks a position survey to summarize the current landscape and draw a roadmap for future development of this promising area. To meet this demand, we present the very first survey paper that reviews and unifies literature of speculative execution in LLMs (e.g., blockwise parallel decoding, speculative decoding, etc.) in a comprehensive framework and a systematic taxonomy. Based on the taxonomy, we present a critical review and comparative analysis of the current arts. Finally we highlight various key challenges and future directions to further develop the area.