Information technology has profoundly altered the way humans interact with information. The vast amount of content created, shared, and disseminated online has made it increasingly difficult to access relevant information. Over the past two decades, recommender systems and search (collectively referred to as information retrieval systems) have evolved significantly to address these challenges. Recent advances in large language models (LLMs) have demonstrated capabilities that surpass human performance in various language-related tasks and exhibit general understanding, reasoning, and decision-making abilities. This paper explores the transformative potential of LLM agents in enhancing recommender and search systems. We discuss the motivations and roles of LLM agents, and establish a classification framework to elaborate on the existing research. We highlight the immense potential of LLM agents in addressing current challenges in recommendation and search, providing insights into future research directions. This paper is the first to systematically review and classify the research on LLM agents in these domains, offering a novel perspective on leveraging this advanced AI technology for information retrieval. To help understand the existing works, we list the existing papers on LLM agent based recommendation and search at this link: https://github.com/tsinghua-fib-lab/LLM-Agent-for-Recommendation-and-Search.